diff --git a/.github/workflows/test_ubuntu.yml b/.github/workflows/test_ubuntu.yml new file mode 100644 index 0000000..33bb550 --- /dev/null +++ b/.github/workflows/test_ubuntu.yml @@ -0,0 +1,51 @@ +# This workflow will install Python dependencies, run tests and lint with a variety of Python versions +# For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions + +name: Test and Coverage (Ubuntu) + +on: + push: + branches: [ master ] + pull_request: + branches: [ master ] + +jobs: + build: + + runs-on: ubuntu-latest + strategy: + fail-fast: false + matrix: + python-version: [3.9] + + steps: + - uses: actions/checkout@v2 + - uses: conda-incubator/setup-miniconda@v2 + with: + auto-update-conda: true + python-version: ${{ matrix.python-version }} + + + - name: Install pip dependencies + run: | + + python -m pip install --upgrade pip + pip install . + pip install -r requirements.txt + python -m pip install flake8 pytest + pip install pytest pytest-cov + pip install coveralls + + - name: Lint with flake8 + run: | + # stop the build if there are Python syntax errors or undefined names + flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics + # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide + flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics + + - name: Test with pytest + run: | + pytest --cov-config=.coveragerc --cov=./ --cov-report=xml + + - name: codecov + uses: codecov/codecov-action@v1 diff --git a/.gitignore b/.gitignore index b6e4761..7abe20a 100644 --- a/.gitignore +++ b/.gitignore @@ -127,3 +127,5 @@ dmypy.json # Pyre type checker .pyre/ +.DS_Store +.vscode/settings.json diff --git a/LICENSE b/LICENSE index 528f4f8..fc7067e 100644 --- a/LICENSE +++ b/LICENSE @@ -1,21 +1,25 @@ -MIT License +BSD 2-Clause License -Copyright (c) 2023 Giulio Rossetti, Salvatore Citraro, Andrea Failla +Copyright (c) 2017, Giulio Rossetti +All rights reserved. -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. +* Redistributions of source code must retain the above copyright notice, this + list of conditions and the following disclaimer. -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. +* Redistributions in binary form must reproduce the above copyright notice, + this list of conditions and the following disclaimer in the documentation + and/or other materials provided with the distribution. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" +AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE +FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR +SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, +OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/README.md b/README.md index 3a2b699..bb486fd 100644 --- a/README.md +++ b/README.md @@ -1,56 +1 @@ # Attributed Stream Hypergraph (ASH) -[![Code style: black](https://img.shields.io/badge/code%20style-black-000000.svg)](https://github.com/psf/black) -[![Documentation Status](https://readthedocs.org/projects/ash-model/badge/?version=latest)](https://ash-model.readthedocs.io//en/latest/?badge=latest) -[![pyversions](https://img.shields.io/pypi/pyversions/ash-model.svg)](https://badge.fury.io/py/ash-model) -[![PyPI version](https://badge.fury.io/py/ash-model.svg)](https://badge.fury.io/py/ash-model) -[![SBD++](https://img.shields.io/badge/Available%20on-SoBigData%2B%2B-green)](https://sobigdata.d4science.org/group/sobigdata-gateway/explore?siteId=20371853) - -![plot](./docs/ASH_logo_full.png) - -``ASH`` is a Python software package that allows to represent and analyze dynamic hypergraphs enriched with node attributes. - - -If you use ``ASH`` as support to your research consider citing: - -> A. Failla, S. Citraro, G. Rossetti -> -> **Attributed Stream Hypergraphs: temporal modeling of node-attributed high-order interactions.** -> -> [arXiv:2303.18226](https://arxiv.org/abs/2303.18226) -> 2023 - -## Tutorial and Online Environments - -Check out the official [tutorial](https://ash-model.readthedocs.io/en/latest/tutorial.html) to get started! - -If you would like to test ``ASH`` functionalities without installing anything on your machine consider using the preconfigured Jupyter Hub instances offered by [SoBigData++](https://sobigdata.d4science.org/group/sobigdata-gateway/explore?siteId=20371853). - -## Installation - -``ASH`` *requires* python>=3.9. - -To install the latest version of our library just download (or clone) the current project, open a terminal and run the following commands: - -```bash -pip install -r requirements.txt -pip install . -``` - -Alternatively use pip -```bash -pip install ash_model -``` - -or conda -```bash -conda config --add channels giuliorossetti -conda config --add channels conda-forge -conda install ash_model -``` - -## Collaborate with us! - -``ASH`` is an active project, any contribution is welcome! - -If you like to include your model in ASH feel free to fork the project, open an issue and contact us. - diff --git a/ash_model/__init__.py b/ash_model/__init__.py index ea4dac0..8c6ea9c 100644 --- a/ash_model/__init__.py +++ b/ash_model/__init__.py @@ -1,4 +1,19 @@ from __future__ import absolute_import -import ash_model.classes +__version__ = "1.0.0" + +# from ash_model import classes, generators, measures, paths, readwrite, utils from ash_model.classes import ASH, NProfile +from ash_model.classes.presence_store import ( + PresenceStore, + DensePresenceStore, + IntervalPresenceStore, +) + +__all__ = [ + "ASH", + "NProfile", + "PresenceStore", + "DensePresenceStore", + "IntervalPresenceStore", +] diff --git a/ash_model/classes/__init__.py b/ash_model/classes/__init__.py index 4dbccc7..1159437 100644 --- a/ash_model/classes/__init__.py +++ b/ash_model/classes/__init__.py @@ -1,2 +1,3 @@ from .undirected import ASH from .node_profile import NProfile +from .presence_store import DensePresenceStore, IntervalPresenceStore diff --git a/ash_model/classes/node_profile.py b/ash_model/classes/node_profile.py index d618203..9cafd96 100644 --- a/ash_model/classes/node_profile.py +++ b/ash_model/classes/node_profile.py @@ -1,203 +1,227 @@ import json +from typing import Any, Dict, List, Optional, Tuple, Union -class NProfile(object): +class NProfile: """ - Node Profile representation. A node profile encloses attributes and statistics of a node. - - :param node_id: a node's unique identifier - :param kwargs: attributes to be added at creation + A profile holding attributes and computed statistics for a node. """ - def __init__(self, node_id: int = None, **kwargs): - self.__attrs = {} + def __init__(self, node_id: Optional[int] = None, **kwargs: Any) -> None: + """ + Initialize a new NProfile. + + :param node_id: Optional identifier for the node. + :param kwargs: Initial attributes to set on the profile. + + """ + self.__attrs: Dict[str, Any] = {} + self.__stats: Dict[str, Dict[str, float]] = {} + self.node_id: Optional[int] = node_id self.add_attributes(**kwargs) - self.__stats = {} - self.node_id = node_id - def add_attribute(self, key: str, value: object) -> None: + def add_attribute(self, key: str, value: Any) -> None: """ - Sets attribute to node profile. + Add or update a single attribute in the profile. + + :param key: Name of the attribute to add. + :param value: Value of the attribute. - :param key: attribute name - :param value: attribute value - :return: """ self.__attrs[key] = value - def add_attributes(self, **kwargs) -> None: + def add_attributes(self, **kwargs: Any) -> None: """ - Sets attributes to node profile. + Add or update multiple attributes in the profile. + + :param kwargs: Key-value pairs of attributes to add. - :param kwargs: dict keyed by attribute name to be added - :return: """ for key, value in kwargs.items(): self.add_attribute(key, value) - def get_attribute(self, key: str) -> object: + def get_attribute(self, key: str) -> Union[str, int, float]: """ - Returns node attribute in the form of a tid : attribute_value dict. Raises ValueError if the attribute is not - found :param key: attribute name :return: + Retrieve the value of a given attribute. + + :param key: Name of the attribute to retrieve. + + :return: The attribute's value. + + :raises ValueError: If the attribute is not present. + """ if key in self.__attrs: - return self.__attrs[key] - raise ValueError(f"Attribute {key} not present in the profile.") + return self.__attrs[key] # type: ignore + raise ValueError(f"Attribute '{key}' not present in the profile.") - def get_attributes(self) -> dict: + def get_attributes(self) -> Dict[str, Any]: """ - Returns all node attributes as key:value pairs. Values are dictionaries keyed by temporal id. + Retrieve all attributes in the profile. + + :return: Dictionary of attribute names to values. - :return: the node's dict of attributes """ - return self.__attrs + return dict(self.__attrs) def has_attribute(self, key: str) -> bool: """ - Checks if the Node Profile has attribute :key: + Check if an attribute exists in the profile. + + :param key: Name of the attribute to check. + + :return: True if the attribute exists, False otherwise. - :param key: attribute name - :return: True if the Node Profile has the attribute, False otherwise. """ return key in self.__attrs def add_statistic(self, attr_name: str, stat_name: str, value: float) -> None: """ - Adds a statistic related to a node attribute + Add or update a computed statistic for a given attribute. - :param attr_name: attribute name - :param stat_name: statistic value - :param value: statistic value - :return: - """ + :param attr_name: The attribute to which the statistic applies. + :param stat_name: Name of the statistic (e.g., 'mean', 'max'). + :param value: Numeric value of the statistic. - if attr_name not in self.__attrs: - raise ValueError(f"{attr_name} not present in the profile") + :raises ValueError: If the attribute is not present in the profile. - if attr_name in self.__stats: - self.__stats[attr_name][stat_name] = value - else: - self.__stats[attr_name] = {stat_name: value} + """ + if attr_name not in self.__attrs: + raise ValueError(f"Attribute '{attr_name}' not present in the profile.") + self.__stats.setdefault(attr_name, {})[stat_name] = value - def get_statistic(self, attr_name: str, stats_name: str = None) -> dict: + def get_statistic( + self, attr_name: str, stats_name: Optional[str] = None + ) -> Dict[str, float]: """ - Returns a statistic related to a node attribute, in the form of stat_name: stat_value pairs. + Retrieve computed statistics for a given attribute. + + :param attr_name: The attribute whose statistics to retrieve. + :param stats_name: Specific statistic name to retrieve (optional). + + :return: Dictionary of statistic names to their values. + + :raises ValueError: If the attribute or statistic is not present. - :param attr_name: attribute name - :param stats_name: statistic name - :return: dictionary with the statistic """ if attr_name not in self.__attrs: - raise ValueError(f"{attr_name} not present in the profile") - + raise ValueError(f"Attribute '{attr_name}' not present in the profile.") if attr_name not in self.__stats: - raise ValueError(f"{attr_name} does not have any computed statistic") - + raise ValueError(f"No statistics computed for attribute '{attr_name}'.") if stats_name is None: - return self.__stats[attr_name] - else: - if stats_name in self.__stats[attr_name]: - return {stats_name: self.__stats[attr_name][stats_name]} - else: - raise ValueError(f"{stats_name} is not computed for {attr_name}") + return dict(self.__stats[attr_name]) + if stats_name in self.__stats[attr_name]: + return {stats_name: self.__stats[attr_name][stats_name]} + raise ValueError( + f"Statistic '{stats_name}' not computed for attribute '{attr_name}'." + ) def has_statistic(self, attr_name: str, stats_name: str) -> bool: """ - Checks if the Node Profile has statistic :stats_name: for attribute :attr_name: + Check if a specific statistic exists for a given attribute. + + :param attr_name: The attribute to check. + :param stats_name: The statistic name to check. + + :return: True if the statistic exists, False otherwise. + + :raises ValueError: If the attribute is not present. - :param attr_name: attribute name - :param stats_name: statistic name - :return: True if the Node Profile has the statistic for the attribute, False otherwise. """ if attr_name not in self.__attrs: - raise ValueError(f"{attr_name} not present in the profile") - - if attr_name not in self.__stats: - return False - if stats_name not in self.__stats[attr_name]: - return False - return True + raise ValueError(f"Attribute '{attr_name}' not present in the profile.") + return stats_name in self.__stats.get(attr_name, {}) - def attribute_computed_statistics(self, attr_name: str) -> list: + def attribute_computed_statistics(self, attr_name: str) -> List[str]: """ - Returns the Node Profile statistics' names computed for :attr_name: + List all computed statistic names for a given attribute. + + :param attr_name: The attribute to query. + + :return: List of statistic names. + + :raises ValueError: If the attribute is not present or has no statistics. - :param attr_name: attribute name - :return: list of the statistics' names computed for the Node Profile """ if attr_name not in self.__attrs: - raise ValueError(f"{attr_name} not present in the profile") + raise ValueError(f"Attribute '{attr_name}' not present in the profile.") if attr_name not in self.__stats: - raise ValueError(f"{attr_name} does not have any computed statistic") + raise ValueError(f"No statistics computed for attribute '{attr_name}'.") return list(self.__stats[attr_name].keys()) - def items(self) -> list: + def items(self) -> List[Tuple[str, Any]]: """ + Get all attribute key-value pairs as a list. + + :return: List of tuples (key, value). - :return: """ - return self.get_attributes().items() + return list(self.__attrs.items()) def __eq__(self, other: object) -> bool: """ + Check equality of two profiles based on their attributes. + + :param other: Another object to compare against. + + :return: True if the other object is an NProfile with identical attributes. - :param other: - :return: """ + if not isinstance(other, NProfile): + return NotImplemented for key, value in self.__attrs.items(): - if not other.has_attribute(key): - return False - - value2 = other.get_attribute(key) - if value != value2: + if not other.has_attribute(key) or other.get_attribute(key) != value: return False return True def __ge__(self, other: object) -> bool: """ + Compare if all numeric attributes of this profile are greater than or equal to those of another. + + :param other: Another NProfile to compare to. + + :return: True if for every non-string attribute, this value >= other's value. - :param other: - :return: """ + if not isinstance(other, NProfile): + return NotImplemented for key, value in self.__attrs.items(): - if not isinstance(value, str): - if not other.has_attribute(key): - return False - - value2 = other.get_attribute(key) - if value < value2: + if isinstance(value, (int, float)): + if not other.has_attribute(key) or value < other.get_attribute(key): return False return True def __le__(self, other: object) -> bool: """ + Compare if all numeric attributes of this profile are less than or equal to those of another. + + :param other: Another NProfile to compare to. + + :return: True if for every non-string attribute, this value <= other's value. - :param other: - :return: """ + if not isinstance(other, NProfile): + return NotImplemented for key, value in self.__attrs.items(): - if not isinstance(value, str): - if not other.has_attribute(key): - return False - - value2 = other.get_attribute(key) - if value > value2: + if isinstance(value, (int, float)): + if not other.has_attribute(key) or value > other.get_attribute(key): return False return True def __str__(self) -> str: """ + Return a JSON-formatted string of all attributes. + + :return: Pretty-printed JSON string of attributes. - :return: """ return json.dumps(self.__attrs, indent=2) - def to_dict(self) -> dict: + def to_dict(self) -> Dict[str, Any]: """ - Returns a dict representation of the Node Profile + Convert the profile to a dictionary representation. - :return: - """ - descr = {"node_id": self.node_id, "attrs": self.__attrs} + :return: Dictionary with 'node_id' and 'attrs' keys. - return descr + """ + return {"node_id": self.node_id, "attrs": dict(self.__attrs)} diff --git a/ash_model/classes/presence_store.py b/ash_model/classes/presence_store.py new file mode 100644 index 0000000..30f4062 --- /dev/null +++ b/ash_model/classes/presence_store.py @@ -0,0 +1,431 @@ +from __future__ import annotations + +"""presence_store.py +~~~~~~~~~~~~~~~~~~~~ +Tiny abstraction layer that lets **ASH** swap the internal representation of +*temporal presence* without touching the public API. + +Only the very small subset of dictionary behaviour used by ``ASH`` is +re‑implemented: + +* ``__getitem__(t)`` – return the set of IDs present at *t* (read‑only). +* ``setdefault(t, set())`` – return a *mutable* set‑like proxy so that calls + like ``self._snapshots.setdefault(t, set()).add(hid)`` keep working. +* ``get(t, default)`` – same semantics as ``dict.get``. +* ``keys()`` – iterable of snapshot indices. + +Two concrete stores are provided: + +* :class:`DensePresenceStore` – thin subclass of ``defaultdict(set)`` that + keeps a *dense* mapping ``time → set[id]``. This + is the default behavior. +* :class:`IntervalPresenceStore` – keeps ``id → list[(start, end)]`` disjoint + intervals and a tiny ``time_counts`` map so that ``keys()`` is cheap. + +Switching the back‑end is as simple as: + +>>> h = ASH(backend="interval") + +No other public API changed. +""" + +from abc import ABC, abstractmethod +from collections import defaultdict +from typing import Dict, Iterable, Iterator, List, Set, Tuple + +############################################################################### +# Abstract façade +############################################################################### + + +class PresenceStore(ABC): + """Minimal dict‑like interface required by :class:`ASH`.""" + + # --------------------------------------------------------------------- + # Required by ASH + # --------------------------------------------------------------------- + + @abstractmethod + def __getitem__(self, t: int) -> Set[int]: + """Return **read‑only** snapshot set for *t*.""" + + @abstractmethod + def setdefault(self, t: int, default: Set[int]) -> "_SnapshotMutable": + """Return mutable set‑like view (creates snapshot if absent).""" + + @abstractmethod + def get(self, t: int, default): + """Dict‑style *get*.""" + + @abstractmethod + def keys(self) -> Iterable[int]: + """Return iterable of snapshot indices.""" + + # ------------------------------------------------------------------ + # Convenience – these are never called directly by ASH but make the + # façade quack like a normal dict. + # ------------------------------------------------------------------ + + def __contains__(self, key: int) -> bool: # pragma: no cover – trivial + return key in self.keys() + + def __iter__(self) -> Iterator[int]: # pragma: no cover – trivial + return iter(self.keys()) + + def __len__(self) -> int: # pragma: no cover – trivial + return len(list(self.keys())) + + +############################################################################### +# Dense implementation (status quo) +############################################################################### + + +class DensePresenceStore(defaultdict, PresenceStore): + """Keep the original *dense* mapping ``time → set[id]`` intact.""" + + def __init__(self): + super().__init__(set) + + # defaultdict already provides all behaviours we need. The overrides + # below are just for static typing clarity. + + def __getitem__(self, t: int) -> Set[int]: # type: ignore[override] + return super().__getitem__(t) + + def setdefault(self, t: int, default: Set[int]) -> Set[int]: # type: ignore[override] + return super().setdefault(t, default) + + +############################################################################### +# Interval implementation +############################################################################### + + +class _SnapshotMutable(set): + """A *mutable* view returned by :meth:`IntervalPresenceStore.setdefault`.""" + + __slots__ = ("_store", "_time") + + def __init__(self, store: "IntervalPresenceStore", time: int, data: Set[int]): + super().__init__(data) # materialised copy so we can do normal set ops + self._store = store + self._time = time + + # Mutators – keep the interval representation in sync ----------------- + + def add(self, element: int): # type: ignore[override] + if element not in self: + super().add(element) + self._store._add_occurrence(element, self._time) + + def discard(self, element: int): # type: ignore[override] + if element in self: + super().discard(element) + self._store._remove_occurrence(element, self._time) + + def remove(self, element: int): # type: ignore[override] + if element not in self: + raise KeyError(element) + self.discard(element) + + +class IntervalPresenceStore(PresenceStore): + """Sparse *interval* representation. + + Internally we keep: + + ``_intervals`` – mapping ``id → List[(start, end)]`` (sorted, disjoint). + ``_starts`` – mapping ``id → List[start]`` (parallel to intervals, for bisect). + ``_time_events`` – difference array ``time → delta`` for O(1) interval updates. + ``_time_counts`` – rebuilt lazily from ``_time_events`` when needed. + + Optimizations: + - Binary search (bisect) for presence checks: O(log k) per id. + - Event-diff updates: O(1) per interval add/remove (vs O(length)). + """ + + def __init__(self): + self._intervals: Dict[int, List[Tuple[int, int]]] = defaultdict(list) + self._starts: Dict[int, List[int]] = defaultdict(list) # for bisect + self._time_events: Dict[int, int] = defaultdict(int) # difference array + self._time_counts: Dict[int, int] = {} + self._time_counts_valid: bool = True # lazy rebuild flag + + # ------------------------------------------------------------------ + # Public façade – dict‑like behaviour expected by ASH + # ------------------------------------------------------------------ + + def __getitem__(self, t: int) -> Set[int]: # noqa: Dunder – matches dict API + """Return *read‑only* snapshot (materialised as an ordinary set).""" + return self._materialise(t) + + def setdefault(self, t: int, default: Set[int]): # noqa: Dunder + """Return *mutable* view for snapshot *t* (creates if absent).""" + # Ensures time bucket exists so later *discard* knows "empty" means + # absence, not "store unaware". + if t not in self._time_counts: + self._time_counts[t] = 0 # really empty snapshot for now + return _SnapshotMutable(self, t, self._materialise(t)) + + def get(self, t: int, default): # noqa: Dunder – dict API + return self._materialise(t) if t in self else default + + def keys(self) -> Iterable[int]: # noqa: Dunder – dict API + self._ensure_time_counts() + return self._time_counts.keys() + + # ------------------------------------------------------------------ + # Internals + # ------------------------------------------------------------------ + + def _ensure_time_counts(self) -> None: + """Rebuild _time_counts from _time_events (lazy reconstruction).""" + if self._time_counts_valid: + return + self._time_counts.clear() + if not self._time_events: + self._time_counts_valid = True + return + + # Compute running count and track all times with positive count + running = 0 + sorted_events = sorted(self._time_events.items()) + if not sorted_events: + self._time_counts_valid = True + return + + # Build ranges where count > 0 + current_t = sorted_events[0][0] + for t, delta in sorted_events: + # Fill in all times from current_t to t-1 with running count + if running > 0: + for tt in range(current_t, t): + self._time_counts[tt] = running + running += delta + current_t = t + + self._time_counts_valid = True + + # ---------- helpers for snapshot (de)materialisation ----------------- + + def _materialise(self, t: int) -> Set[int]: + """Compute *set* of IDs alive at time *t* using bisect (O(log k) per id).""" + import bisect + + present: Set[int] = set() + for hid, intervals in self._intervals.items(): + if not intervals: + continue + starts = self._starts[hid] + # bisect_right(starts, t) gives index of first start > t + i = bisect.bisect_right(starts, t) - 1 + if i >= 0: + s, e = intervals[i] + if s <= t <= e: + present.add(hid) + return present + + # ---------- mutators ------------------------------------------------- + + def _add_occurrence(self, hid: int, t: int) -> None: + """Insert a *single* time‑point into ``hid``'s interval list.""" + intervals = self._intervals[hid] + starts = self._starts[hid] + + # Check if already present + already_present = False + for s, e in intervals: + if s <= t <= e: + already_present = True + break + + if already_present: + return # nothing to do + + # Find merge candidates and apply + if not intervals: # first ever + intervals.append((t, t)) + starts.append(t) + self._time_events[t] += 1 + self._time_events[t + 1] -= 1 + self._time_counts_valid = False + return + + merged = False + for i, (s, e) in enumerate(intervals): + # Extend forward + if t == e + 1: + intervals[i] = (s, t) + # Merge with next if adjacent + if i + 1 < len(intervals) and intervals[i + 1][0] == t + 1: + n_s, n_e = intervals.pop(i + 1) + starts.pop(i + 1) + intervals[i] = (s, n_e) + # Net event: only t gets added (merging doesn't change event counts elsewhere) + else: + # Just extending: add t + self._time_events[t] += 1 + self._time_events[t + 1] -= 1 + merged = True + break + # Extend backward + if t == s - 1: + intervals[i] = (t, e) + starts[i] = t + # Merge with previous if adjacent + if i - 1 >= 0 and intervals[i - 1][1] == t - 1: + p_s, p_e = intervals.pop(i - 1) + starts.pop(i - 1) + intervals[i - 1] = (p_s, e) + starts[i - 1] = p_s + # Net event: only t gets added + else: + self._time_events[t] += 1 + self._time_events[t + 1] -= 1 + merged = True + break + if t < s - 1: + intervals.insert(i, (t, t)) + starts.insert(i, t) + self._time_events[t] += 1 + self._time_events[t + 1] -= 1 + merged = True + break + + if not merged: + intervals.append((t, t)) + starts.append(t) + self._time_events[t] += 1 + self._time_events[t + 1] -= 1 + + self._time_counts_valid = False + + def _remove_occurrence(self, hid: int, t: int) -> None: + """Remove a single time‑point from ``hid``'s intervals (if present).""" + intervals = self._intervals.get(hid, []) + starts = self._starts.get(hid, []) + + found = False + for i, (s, e) in enumerate(intervals): + if s <= t <= e: + found = True + if s == e == t: # whole interval goes away + intervals.pop(i) + starts.pop(i) + elif t == s: # shrink from left + intervals[i] = (s + 1, e) + starts[i] = s + 1 + elif t == e: # shrink from right + intervals[i] = (s, e - 1) + else: # split interval in two + intervals[i] = (s, t - 1) + intervals.insert(i + 1, (t + 1, e)) + starts.insert(i + 1, t + 1) + break # done + + if found: + # Update time events (difference array) + self._time_events[t] -= 1 + self._time_events[t + 1] += 1 + self._time_counts_valid = False + + def _add_interval(self, hid: int, start: int, end: int) -> None: + """Insert the entire [start,end] span into ``hid``'s interval list in one pass.""" + intervals = self._intervals[hid] + starts = self._starts[hid] + + # Track old coverage before merge + old_intervals = list(intervals) + + new_s, new_e = start, end + i = 0 + # 1) Merge any overlapping or adjacent existing intervals + merged_indices = [] + while i < len(intervals): + s, e = intervals[i] + if e + 1 < new_s: + i += 1 + continue + if s - 1 > new_e: + break + # overlapping or adjacent -> absorb + new_s = min(new_s, s) + new_e = max(new_e, e) + merged_indices.append(i) + i += 1 + + # Remove merged intervals in reverse to preserve indices + for idx in reversed(merged_indices): + intervals.pop(idx) + starts.pop(idx) + + # 2) Insert the merged interval at the correct position + insert_pos = len([s for s in starts if s < new_s]) + intervals.insert(insert_pos, (new_s, new_e)) + starts.insert(insert_pos, new_s) + + # 3) Update events: add for [new_s, new_e], subtract for old intervals that were merged + self._time_events[new_s] += 1 + self._time_events[new_e + 1] -= 1 + + for idx in merged_indices: + old_s, old_e = old_intervals[idx] + self._time_events[old_s] -= 1 + self._time_events[old_e + 1] += 1 + + self._time_counts_valid = False + + def _remove_interval(self, hid: int, start: int, end: int) -> None: + """Remove the entire [start,end] span from ``hid``'s interval list in one pass.""" + intervals = self._intervals.get(hid, []) + starts = self._starts.get(hid, []) + + # Track old intervals that will be affected + old_intervals = list(intervals) + affected_indices = [] + + i = 0 + to_insert = [] + indices_to_remove = [] + while i < len(intervals): + s, e = intervals[i] + if e < start or s > end: + i += 1 + continue + # overlapping: may need to split or shrink + affected_indices.append(i) + before = (s, start - 1) if s < start else None + after = (end + 1, e) if e > end else None + indices_to_remove.append(i) + if before: + to_insert.append((i, before)) + if after: + to_insert.append((i, after)) + i += 1 + + # Remove old intervals in reverse + for idx in reversed(indices_to_remove): + intervals.pop(idx) + starts.pop(idx) + + # Insert new split intervals + for idx, (new_s, new_e) in to_insert: + insert_pos = len([s for s in starts if s < new_s]) + intervals.insert(insert_pos, (new_s, new_e)) + starts.insert(insert_pos, new_s) + + # Update events: remove [start, end], add back the split pieces + self._time_events[start] -= 1 + self._time_events[end + 1] += 1 + + for idx in affected_indices: + old_s, old_e = old_intervals[idx] + self._time_events[old_s] -= 1 + self._time_events[old_e + 1] += 1 + + for _, (new_s, new_e) in to_insert: + self._time_events[new_s] += 1 + self._time_events[new_e + 1] -= 1 + + self._time_counts_valid = False diff --git a/ash_model/classes/undirected.py b/ash_model/classes/undirected.py index 1633732..587d3f0 100644 --- a/ash_model/classes/undirected.py +++ b/ash_model/classes/undirected.py @@ -1,1265 +1,1825 @@ -import json +from __future__ import annotations + from collections import defaultdict from itertools import combinations +from typing import ( + Any, + DefaultDict, + Dict, + Generator, + Iterable, + List, + Optional, + Set, + Tuple, + Union, +) import networkx as nx -from halp.undirected_hypergraph import UndirectedHypergraph from .node_profile import NProfile +from .presence_store import DensePresenceStore, IntervalPresenceStore, PresenceStore -class ASH(object): - """ - Class for representing the Attributed Stream Hypergraph. +class ASH: + def __init__( + self, + backend: str = "dense", + ) -> None: + """ + Initialize an ASH (Attributed Stream Hypergraph) instance. - :param hedge_removal: whether to allow for hyperedge removal or not - """ + :param backend: The backend for storing temporal information on hyperedges. Supported values are "dense" (stores time → set[id]) and "interval" (stores id → list[(start, end)] disjoint intervals). + :raises ValueError: If an unsupported backend is specified. - def __init__(self, hedge_removal: bool = False) -> None: - self.H = UndirectedHypergraph() - self.time_to_edge = defaultdict(lambda: defaultdict(str)) - self.snapshots = {} - self.hedge_removal = hedge_removal + Examples + -------- + .. code-block:: python - def __recursive_merge(self, inter: list, start_index: int = 0) -> list: - """ + from ash_model.classes.undirected import ASH - :param inter: - :param start_index: - :return: - """ - for i in range(start_index, len(inter) - 1): - if inter[i][1] > inter[i + 1][0]: - new_start = inter[i][0] - new_end = inter[i + 1][1] - inter[i] = [new_start, new_end] - del inter[i + 1] - return self.__recursive_merge(inter.copy(), start_index=i) - return inter + # Dense (default) backend + H = ASH() + + # Interval backend + H2 = ASH(backend="interval") - def temporal_snapshots_ids(self) -> list: """ - Returns the list of temporal snapshots ids for the ASH, i.e., - integers representing points in time. - :return: list of temporal ids + if backend == "dense": + self._snapshots: PresenceStore = DensePresenceStore() + elif backend == "interval": + self._snapshots: PresenceStore = IntervalPresenceStore() + else: + raise ValueError("backend must be 'dense' or 'interval' (got %r)" % backend) + + # edge data + self._current_hyperedge_id: int = 0 + self._eid2nids: Dict[str, frozenset[int]] = {} + self._nids2eid: Dict[frozenset[int], str] = {} + + # {eid : {attr_name: value}} + self._edge_attributes: DefaultDict[str, DefaultDict[int, Dict[str, Any]]] = ( + defaultdict(lambda: defaultdict(dict)) + ) + + # node data + self._node_attrs: DefaultDict[int, DefaultDict[int, Dict[str, Any]]] = ( + defaultdict(lambda: defaultdict(dict)) + ) + self._stars: DefaultDict[int, Set[str]] = defaultdict(set) + + # ------------------------------------------------------------------ + # Utility methods + # ------------------------------------------------------------------ + + def __presence_to_intervals(self, presence: List[int]) -> List[Tuple[int, int]]: + """Convert a list of time instants into contiguous intervals.""" + presence = sorted(presence) + intervals: List[Tuple[int, int]] = [] + start = presence[0] + end = presence[0] + + for i in range(1, len(presence)): + if presence[i] == end + 1: + end = presence[i] + else: + intervals.append((start, end)) + start = presence[i] + end = presence[i] + + intervals.append((start, end)) + return intervals + + def __time_window(self, start: Optional[int], end: Optional[int]) -> List[int]: + if start is None: + return self.temporal_snapshots_ids() + if end is None: + end = start + return list(range(start, end + 1)) + + # ------------------------------------------------------------------ + # Iterators / Streams + # ------------------------------------------------------------------ + + def temporal_snapshots_ids(self) -> List[int]: + """ + Return a sorted list of all temporal snapshot ids (time instants) in the ASH. + This method retrieves the keys from the internal snapshot store, which + represent the time instants when hyperedges are present. + + :return: Sorted list of temporal snapshot ids. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, 0) + H.add_node(2, 0) + H.add_hyperedge([1, 2], start=0) + tids = H.temporal_snapshots_ids() # e.g., [0] + + """ + return sorted(self._snapshots.keys()) + + def stream_interactions(self) -> Generator[Tuple[int, str, str], None, None]: + """ + Generate a stream of interactions in the ASH, yielding tuples of the form + (time_id, hyperedge_id, event_type), where event_type is either + "+" for activation or "-" for deactivation of a hyperedge at that time. + This method iterates through the temporal snapshots and compares the sets + of hyperedges present in consecutive snapshots to determine hyperedge changes. + + :yield: Tuples of (time_id, hyperedge_id, event_type). + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, 0, 1) + H.add_node(2, 0, 1) + H.add_hyperedge([1, 2], start=0, end=1) + events = list(H.stream_interactions()) + # Example output: [(0, 'e1', '+'), (1, 'e1', '-')] + + """ + tids = self.temporal_snapshots_ids() + if not tids: + return + # First snapshot – pure additions + for hid in self._snapshots[tids[0]]: + yield tids[0], hid, "+" + # Subsequent diffs + for t in tids[1:]: + prev, curr = self._snapshots[t - 1], self._snapshots[t] + for hid in curr - prev: + yield t, hid, "+" + for hid in prev - curr: + yield t, hid, "-" + + def add_hyperedge( + self, + nodes: Iterable[int], + start: int, + end: Optional[int] = None, + **kwargs: Any, + ) -> None: """ - return sorted(self.snapshots.keys()) + Add a hyperedge to the ASH. If nodes are not already present, they will be added. + If end time is not specified, then the hyperedge is considered to be present only at `start` (end = start). + + :param nodes: Iterable of node IDs that form the hyperedge. + :param start: Start time of the hyperedge. + :param end: End time of the hyperedge (inclusive). If None, the hyperedge is considered to be present only at `start`. + :param kwargs: Optional attributes for the hyperedge. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, 0) + H.add_node(2, 0) + H.add_hyperedge([1, 2], start=0, weight=3) + list(H.hyperedges()) # ['e1'] + H.get_hyperedge_weight('e1') # 3 - def stream_interactions(self) -> list: """ - The stream_interactions function yields a list of tuples, - where each tuple contains three elements identifying interaction appearance/disappearance. - The first element is a temporal snapshot id. The second is a hyperedege id. The third - is either '+' (if the hyperedge appears) or '-' (if the hyperedge disappears). - :return: A generator that yields the time, hyperedge_id, and appearance/disappearance - for each interaction in the stream + span = (start, start if end is None else end) + f_nodes = frozenset(nodes) + + # Either fetch existing or mint a new hyperedge id ---------------- + if f_nodes in self._nids2eid: + hid = self._nids2eid[f_nodes] + else: + self._current_hyperedge_id += 1 + hid = f"e{self._current_hyperedge_id}" + self._eid2nids[hid] = f_nodes + self._nids2eid[f_nodes] = hid + for n in f_nodes: + # Ensure node exists for the span (dummy attrs if absent) + if n not in self._node_attrs: + self.add_node(n, span[0], span[1]) + else: + for t in range(span[0], span[1] + 1): + if t not in self._node_attrs[n]: + self.add_node(n, t) + self._stars[n].add(hid) + + # Register presence ------------------------------------------------ + if isinstance(self._snapshots, IntervalPresenceStore): + self._snapshots._add_interval(hid, span[0], span[1]) + else: + for t in range(span[0], span[1] + 1): + self._snapshots.setdefault(t, set()).add(hid) + + # Store attributes ------------------------------------------------- + if "weight" not in kwargs: + kwargs["weight"] = 1 + + for k, v in kwargs.items(): + self._edge_attributes[hid][k] = v + + def add_hyperedges( + self, + hyperedges: Iterable[Iterable[int]], + start: int, + end: Optional[int] = None, + **kwargs: Any, + ) -> None: """ + Add multiple hyperedges to the ASH. If nodes are not already present, they will be added. + All hyperedges will be added with the same start and end times. + if `end` is not specified, then the hyperedges are considered to be present only at `start` (end = start). - keys = sorted(self.time_to_edge.keys()) - for tid in keys: - for he, op in self.time_to_edge[tid].items(): - yield tid, he, op + :param hyperedges: Iterable of iterables, where each inner iterable contains node IDs for a hyperedge. + :param start: Start time of the hyperedges. + :param end: End time of the hyperedges (inclusive). If None, the hyperedges are considered to be present only at `start`. + :param kwargs: Optional attributes for the hyperedges. These will be applied to all hyperedges. - ## Nodes + Examples + -------- + .. code-block:: python - def avg_number_of_nodes(self) -> float: - """ - The avg_number_of_nodes function returns the average number of nodes in an ASH over time, i.e., the - sum of each snapshot's nodes divided by the number of snapshots. + H = ASH() + H.add_nodes([1, 2, 3, 4], start=0) + H.add_hyperedges([[1, 2], [2, 3, 4]], start=0) + H.number_of_hyperedges() # 2 - :return: The average number of nodes in the ASH over all snapshots """ - nodes_snapshots = [ - self.get_number_of_nodes(tid) for tid in self.snapshots.keys() - ] - return sum(nodes_snapshots) / len(self.snapshots.keys()) + for hedge in hyperedges: + self.add_hyperedge(hedge, start, end, **kwargs) + + # ------------------------------------------------------------------ + # Node management + # ------------------------------------------------------------------ def add_node( - self, node: int, start: int, end: int = None, attr_dict: object = None + self, + node: int, + start: int, + end: Optional[int] = None, + attr_dict: Optional[Union[Dict[str, Any], NProfile]] = None, ) -> None: """ - The add_node function adds a node to the ASh. - It takes as input: - -node, an integer representing the node to be added; - -start, an integer representing the start of the interval in which this node is active; - -end, an optional argument that represents the end of interval in which this node is active - (if not specified it defaults to start); and - -attr_dict, a dictionary containing attributes associated with this particular node. + Add a node to the ASH with optional attributes. + Attributes can be provided as a dictionary of the form {attr_name: value} or as an NProfile instance. + If the node is not already present, it will be created with the specified attributes. + If end time is not specified, then the node is considered to be present only at `start` (end = start). - :param node: Identify the node - :param start: Specify the starting snapshot of the node - :param end: Specify the end of the interval - :param attr_dict: dictionary of attributes to be added to the node's profile - :return: + To add a node with different attributes at different times, you can call this method multiple times with different `start` and `end` values. - """ + :param node: Node ID to add. + :param start: Start time of the node. + :param end: End time of the node (inclusive). If None, the node is considered to be present only at `start`. + :param attr_dict: Optional attributes for the node. Can be a dictionary or an NProfile instance. - if end is None: - start = [start, start] - else: - start = [start, end] + Examples + -------- + .. code-block:: python - if not self.H.has_node(node): - old_attrs = {"t": [start]} - else: - old_attrs = self.H.get_node_attributes(node) - if "t" in old_attrs: - old_attrs["t"].append(start) - else: - old_attrs["t"] = [start] - - head = None - for i in range(start[0], start[1] + 1): - if attr_dict is None: - continue - for key, v in attr_dict.items(): - if key in old_attrs and key != "t": - if head is not None: - old_attrs[key][i] = head - else: - old_attrs[key][i] = v - else: - old_attrs[key] = {i: v} - head = f"t_{i}" - - # compacting intervals - intervals = [] - presence = sorted(old_attrs["t"]) - for i, span in enumerate(presence): - if i < len(presence) - 1: - if span[1] == presence[i + 1][0] - 1: - intervals.append([span[0], presence[i + 1][1]]) - else: - intervals.append(span) - else: - intervals.append(span) + H = ASH() + H.add_node(1, start=0, end=2, attr_dict={"group": "A"}) + H.get_node_attribute(1, "group", tid=0) # 'A' + H.has_node(1, 1) # True - merged = self.__recursive_merge(intervals.copy()) - - # contiguity - cont = [merged[0]] - pos = 0 - for i in range(1, len(merged)): - if cont[pos][1] == merged[i][0]: - cont[pos][1] = merged[i][1] - else: - pos += 1 - cont.append(merged[i]) + """ - old_attrs["t"] = cont + span = (start, start if end is None else end) + attrs_source: Dict[str, Any] + if isinstance(attr_dict, NProfile): + attrs_source = attr_dict.get_attributes() + else: + attrs_source = attr_dict or {} - self.H.add_node(node, old_attrs) - if start[0] not in self.snapshots: - self.snapshots[start[0]] = [] - if end is not None and end not in self.snapshots: - self.snapshots[end] = [] + for t in range(span[0], span[1] + 1): + self._node_attrs[node][t] = dict(attrs_source) + self._snapshots.setdefault(t, set()) # ensure snapshot exists def add_nodes( - self, nodes: list, start: int, end: int = None, node_attr_dict: dict = None + self, + nodes: Iterable[int], + start: int, + end: Optional[int] = None, + node_attr_dict: Optional[Dict[int, Union[NProfile, Dict[str, Any]]]] = None, ) -> None: """ - The add_nodes function adds a list of nodes to the ASH with an optional node-to-attributes - dictionary. All nodes will be assumed to be active in the same time window, defined by :start: and :end: + Add multiple nodes to the ASH with optional attributes. + Attributes can be provided as a dictionary mapping node IDs to their attributes. - :param nodes: Specify the nodes to be added - :param start: Specify the appearance time of the nodes - :param end: Specify the disappearance time of the nodes - :param node_attr_dict: Dictionary of attributes to be added to the nodes. - :return: None - """ + :param nodes: Iterable of node IDs to add. + :param start: Start time of the nodes. + :param end: End time of the nodes (inclusive). If None, the nodes are considered to be present only at `start`. + :param node_attr_dict: Optional dictionary mapping node IDs to their attributes. If None, no attributes are added. + + Examples + -------- + .. code-block:: python - for node in nodes: - attr = None if node not in node_attr_dict else node_attr_dict[node] - self.add_node(node, start, end, attr) + H = ASH() + H.add_nodes([1, 2, 3], start=0, node_attr_dict={1: {"color": "red"}}) + H.number_of_nodes(0) # 3 + H.get_node_attribute(1, "color", 0) # 'red' - def get_node_profile(self, node: int, tid: int = None) -> NProfile: """ - The get_node_profile function returns a copy of the NProfile object associated with the given node. - The optional parameter tid specifies the temporal snapshot the profile refers to. + node_attr_dict = node_attr_dict or {} + for n in nodes: + self.add_node(n, start, end, node_attr_dict.get(n)) + + # ------------------------------------------------------------------ + # Removal helpers + # ------------------------------------------------------------------ - :param node: Specify the node to get the profile of - :param tid: Get the profile of a node at a specific time - :return: A NProfile object + def remove_hyperedge( + self, + hyperedge_id: str, + start: Optional[int] = None, + end: Optional[int] = None, + ) -> None: """ + Remove a hyperedge from the ASH, including its presence in the specified time window. - if tid is None: - attrs = self.H.get_node_attributes(node) - for key, l in attrs.items(): - if key != "t": - for tid, value in l.items(): - if isinstance(value, str) and "t_" in value: - base_tid = int(value[2:]) - attrs[key][tid] = l[base_tid] - - return NProfile(node, **attrs) - else: - res = {} - attrs = self.H.get_node_attributes(node) - for key, l in attrs.items(): - if key != "t" and tid in l: - res[key] = l[tid] - if isinstance(l[tid], str) and "t_" in l[tid]: - base_tid = int(l[tid][2:]) - res[key] = l[base_tid] - return NProfile(node, **res) + :param hyperedge_id: ID of the hyperedge to remove. + :param start: Start time of the removal. If None, the hyperedge is removed from all times. + :param end: End time of the removal (inclusive). If None, the hyperedge is removed only at `start`. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2], start=0) + H.add_hyperedge([1, 2], start=0, end=2) + H.remove_hyperedge('e1', start=1, end=2) + H.has_hyperedge('e1', 0) # True + H.has_hyperedge('e1', 1) # False - def get_node_attribute(self, node: int, attr_name: str, tid: int = None) -> object: """ - The get_node_attribute function returns the value of a node attribute for a given node. - If no temporal snapshot id (tid) is specified, it will return a tid-to-attribute-value - dictionary for that node. - If a tid is specified, it will return the value of the attribute at that tid. - :param node: Specify which node to get the attribute of - :param attr_name: Specify the attribute name - :param tid: Get the attribute for all time steps, or for a specific time step - :return: The attribute of the node. A dict if tid is specified, the attribute value otherwise + # Determine removal spans + if isinstance(self._snapshots, IntervalPresenceStore): + spans = ( + self.hyperedge_presence(hyperedge_id, as_intervals=True) + if start is None + else [(start, start if end is None else end)] + ) + for s, e in spans: + self._snapshots._remove_interval(hyperedge_id, s, e) + # Remove edge attributes for these times + for t in range(s, e + 1): + self._edge_attributes[hyperedge_id].pop(t, None) + else: + time_window = set(self.__time_window(start, end)) + for t in self.temporal_snapshots_ids(): + if t in time_window: + self._snapshots.setdefault(t, set()).discard(hyperedge_id) + self._edge_attributes[hyperedge_id].pop(t, None) + + # Cleanup metadata if no presence remains + still_exists = False + for t in self.temporal_snapshots_ids(): + if self.has_hyperedge(hyperedge_id, t): + still_exists = True + break + if not still_exists: + nodes = self.get_hyperedge_nodes(hyperedge_id) + del self._eid2nids[hyperedge_id] + del self._nids2eid[nodes] + self._edge_attributes.pop(hyperedge_id, None) + for n in nodes: + self._stars[n].discard(hyperedge_id) + + def remove_hyperedges( + self, + hyperedges: Iterable[str], + start: Optional[int] = None, + end: Optional[int] = None, + ) -> None: """ + Remove multiple hyperedges from the ASH, including their presence in the specified time window. - if tid is None: - attrs = self.H.get_node_attribute(node, attr_name) - if attr_name == "t": - return {"t": attrs} - for tid, value in attrs.items(): - if "t_" in value: - base_tid = int(value[2:]) - attrs[tid] = attrs[base_tid] - return attrs + :param hyperedges: Iterable of hyperedge IDs to remove. + :param start: Start time of the removal. If None, the hyperedges are removed from all times. + :param end: End time of the removal (inclusive). If None, the hyperedges are removed only at `start`. - else: - attrs = self.H.get_node_attribute(node, attr_name) - if attr_name == "t": - for spans in attrs: - for span in spans: - if span[0] <= tid <= span[1] + 1: - return {"t": [attrs]} - return {"t": []} - value = attrs[tid] - if isinstance(value, str) and "t_" in value: - return attrs[int(value[2:])] - return attrs[tid] - - def node_attributes_to_attribute_values( - self, categorical=False, tid: int = None - ) -> dict: - """ - The node_attributes_to_attribute_values function returns a dictionary of the attributes and their values. The - function takes in two parameters: categorical, which is a boolean that determines whether to include - numerical attributes, and tid, which is an integer that represents the temporal id. The default value for - categorical is False and the default value for tid is None. - - :param self: Bind the method to the object - :param categorical: Specify whether the attributes are categorical or not - :param tid: Specify the temporal id - :return: A dictionary of attribute names and the values they can take - """ - - attributes = defaultdict(set) - for n in self.get_node_set(tid=tid): - for name, vals in self.get_node_profile(n, tid=tid).items(): - if name != "t": - if tid is None: - for value in vals.values(): - attributes[name].add(value) - else: - attributes[name].add(vals) - if categorical: - numerical = [ - attribute - for attribute in attributes - if not isinstance(list(attributes[attribute])[0], str) - ] - for attribute in numerical: - del attributes[attribute] + Examples + -------- + .. code-block:: python - return attributes + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [2, 3]], start=0) + ids = H.hyperedges() + H.remove_hyperedges(ids, start=0) + H.number_of_hyperedges(0) # 0 - def get_node_set(self, tid: int = None) -> list: """ - The get_node_set function returns the set of all the nodes in the ASH. - If a snapshot id (tid) is specified, it will return only those nodes that appear in that snapshot. + for hid in hyperedges: + self.remove_hyperedge(hid, start, end) - :param tid: Optional temporal snapshot id - :return: The set of nodes in the ASH + def remove_node( + self, + node: int, + start: Optional[int] = None, + end: Optional[int] = None, + ) -> None: """ + Remove a node from the ASH, including its attributes and all hyperedges it is part of, + in the specified time window. - if tid is None: - return self.H.get_node_set() - else: - return {n for n in self.H.get_node_set() if self.has_node(n, tid)} + :param node: Node ID to remove. + :param start: Start time of the removal. If None, the node is removed from all times. + :param end: End time of the removal (inclusive). If None, the node is removed only at `start`. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2], start=0) + H.add_hyperedge([1, 2], start=0) + H.remove_node(1, start=0) + H.has_node(1, 0) # False - def get_number_of_nodes(self, tid: int = None) -> int: """ - The get_number_of_nodes function returns the number of nodes in the ASH. - If no temporal snapshot id (tid) is specified, it will return the total number of nodes. - Otherwise, it will return the total number of nodes that are active in tid. - :param tid: Optional temporal snapshot id - :return: The number of nodes in the ASH + for t in self.__time_window(start, end): + self._node_attrs[node].pop(t, None) + if not self._node_attrs[node]: + self._node_attrs.pop(node, None) + + for hid in list(self._stars.get(node, [])): + self.remove_hyperedge(hid, start, end) + self._stars.pop(node, None) + + def remove_nodes( + self, + nodes: Iterable[int], + start: Optional[int] = None, + end: Optional[int] = None, + ) -> None: """ + Remove multiple nodes from the ASH, including their attributes and all hyperedges they are part of, + in the specified time window. - if tid is None: - return len(self.get_node_set()) - else: - return len(self.get_node_set(tid)) + :param nodes: Iterable of node IDs to remove. + :param start: Start time of the removal. If None, the nodes are removed from all times. + :param end: End time of the removal (inclusive). If None, the nodes are removed only at `start`. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.remove_nodes([1, 3], start=0) + set(H.nodes(0)) # {2} - def get_star(self, node: int, hyperedge_size: int = None, tid: int = None) -> set: """ - The get_star function returns the set of hyperedge ids that include a given node. - If no hyperedge size is specified, it returns all of the hyperedges that include a given node. - Otherwise, it will return only those with exactly that many nodes. - If temporal snapshot id (tid) is specified, it restricts the star to the hyperedges that are active in tid. - :param node: Specify the node whose star is to be returned - :param hyperedge_size: Optionally restrict star to hyperedges with specific size - :param tid: Optionally restrict star to hyperedges active at a point in time - :return: The set of hyperedge ids that include a given node + for n in nodes: + self.remove_node(n, start, end) + + def remove_unlabelled_nodes( + self, + attr_name: str, + start: Optional[int] = None, + end: Optional[int] = None, + ) -> None: """ + Remove nodes that do not have a specific attribute in the specified time window. + If no time window is specified, the nodes are checked in all times. + + :param attr_name: The name of the attribute to check for. + :param start: Start time of the removal. If None, the nodes are checked in all times. + :param end: End time of the removal (inclusive). If None, the nodes are checked only at `start`. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, 0, attr_dict={"label": "A"}) + H.add_node(2, 0) + H.remove_unlabelled_nodes("label", start=0) + set(H.nodes(0)) # {1} - if tid is None: - eids = self.H.get_star(node) - if hyperedge_size is None: - return eids - else: - return { - eid - for eid in eids - if len(self.get_hyperedge_nodes(eid)) == hyperedge_size - } - else: - if hyperedge_size is None: - return { - eid - for eid in self.H.get_star(node) - if self.has_hyperedge_id(eid, tid) - } - else: - return { - eid - for eid in self.H.get_star(node) - if self.has_hyperedge_id(eid, tid) - and len(self.get_hyperedge_nodes(eid)) == hyperedge_size - } - - def get_number_of_neighbors( - self, node: int, hyperedge_size: int = None, tid: int = None - ) -> int: """ - The get_number_of_neighbors function returns the number of nodes a node is connected to via hyperedges. - If the optional argument hyperedge_size is provided, then only neighbors belonging to hyperedges - of that size will be counted. - The optional argument tid restricts the counting to the nodes connected in a specific temporal snapshot. - :param node: Specify the node whose neighbors are to be counted - :param hyperedge_size: Specify the exact size of the hyperedges to count the nodes of - :param tid:: Specify the temporal snapshot - :return: The number of neighbors for a given node + for node, t_attrs in list(self._node_attrs.items()): + for t in self.__time_window(start, end): + if t in t_attrs and attr_name not in t_attrs[t]: + self.remove_node(node, t, t) + + # ------------------------------------------------------------------ + # Node & Hyperedge queries + # ------------------------------------------------------------------ + + def nodes( + self, start: Optional[int] = None, end: Optional[int] = None + ) -> List[int]: """ - neighbors = self.get_neighbors(node, hyperedge_size, tid) - return len(neighbors) + Return a list of node IDs present in the ASH within the specified time window. + + :param start: Start time of the query. If None, all nodes are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: List of node IDs. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.nodes(0) # [1, 2, 3] (order not guaranteed) - def get_neighbors( - self, node: int, hyperedge_size: int = None, tid: int = None - ) -> set: """ - The get_neighbors function returns the set of all nodes that are connected to a given node via hyperedges. - If the optional argument hyperedge_size is provided, then only neighbors belonging to hyperedges - of that size will be returned. - The optional argument tid restricts the set to the nodes connected in a specific temporal snapshot. + if start is None: + return list(self._node_attrs.keys()) + res: List[int] = [] + if end is None: + for n in self._node_attrs: + if start in self._node_attrs[n]: + res.append(n) + else: + for n in self._node_attrs: + if any(start <= t <= end for t in self._node_attrs[n]): + res.append(n) + return res + + def hyperedges( + self, + start: Optional[int] = None, + end: Optional[int] = None, + hyperedge_size: Optional[int] = None, + as_ids: bool = True, + ) -> List[Union[str, frozenset[int]]]: + """ + Return a list of hyperedge IDs or their node sets present in the ASH within the specified time window. + Hyperedges are identified by their IDs (strings), or by sets of node IDs (frozensets). + If `hyperedge_size` is specified, only hyperedges of that size are returned. + The `as_ids` parameter determines whether to return hyperedge IDs or sets of node IDs. + + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :param hyperedge_size: If specified, only hyperedges of this size are returned. + :param as_ids: If True, return hyperedge IDs; if False, return sets of node IDs. + :return: List of hyperedge IDs or sets of node IDs. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [2, 3]], start=0) + H.hyperedges(0) # e.g., ['e1', 'e2'] + H.hyperedges(0, as_ids=False) # [frozenset({1,2}), frozenset({2,3})] + H.hyperedges(0, hyperedge_size=2) # only size-2 hyperedges - :param node: Specify the node for which we want to get its neighbors - :param hyperedge_size: Specify the size of the hyperedge to be returned - :param tid: Specify a specific transaction id - :return: The set of neighbors of a given node """ + if start is None: + hyperedges_set: Set[str] = set(self._eid2nids.keys()) + else: + hyperedges_set = set() + for t in self.__time_window(start, end): + hyperedges_set.update(self._snapshots[t]) - star = self.get_star(node, tid=tid) - res = [] if hyperedge_size is not None: - for s in star: - nodes = self.get_hyperedge_nodes(s) - if len(nodes) == hyperedge_size: - res.extend(nodes) - else: - for s in star: - nodes = self.get_hyperedge_nodes(s) - res.extend(nodes) - res = set(res) - res.discard(node) - return res + hyperedges_set = { + h + for h in hyperedges_set + if len(self.get_hyperedge_nodes(h)) == hyperedge_size + } + + if as_ids: + return list(hyperedges_set) + return [self._eid2nids[h] for h in hyperedges_set] + + def has_hyperedge( + self, + edge: Union[str, Iterable[int]], + start: Optional[int] = None, + end: Optional[int] = None, + ) -> bool: + """ + Check if a hyperedge is present in the ASH within the specified time window. + Accepts either a hyperedge ID (string) or an iterable of node IDs. + + :param edge: Hyperedge ID (string) or an iterable of node IDs. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: True if the hyperedge is present, False otherwise. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2], start=0) + H.add_hyperedge([1, 2], start=0) + H.has_hyperedge('e1', 0) # True + H.has_hyperedge([1, 2], 0) # True + H.has_hyperedge([2, 3], 0) # False + + """ + + if not isinstance(edge, str): + try: + edge = self.get_hyperedge_id(edge) + except KeyError: + return False + if start is None: + return edge in self._eid2nids + return edge in set(self.hyperedges(start, end)) + + def has_node( + self, node: int, start: Optional[int] = None, end: Optional[int] = None + ) -> bool: + """ + Check if a node is present in the ASH within the specified time window. + + :param node: Node ID to check. + :param start: Start time of the query. If None, all nodes are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: True if the node is present, False otherwise. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, 0) + H.has_node(1, 0) # True + H.has_node(2, 0) # False - def get_degree(self, node: int, hyperedge_size: int = None, tid: int = None) -> int: """ - The get_degree function returns the number of hyperedges that a given node is part of. - If the optional argument hyperedge_size is specified, then it returns only the number - of hyperedges that have exactly this many nodes. + return node in set(self.nodes(start, end)) - :param node: Specify the node id - :param hyperedge_size: Specify the size of hyperedges to be counted - :param tid: Get the degree at a specific point in time - :return: The degree of a node + def get_hyperedge_nodes(self, hyperedge_id: str) -> frozenset[int]: """ - star = self.get_star(node, tid=tid) + Get the set of node IDs that form a hyperedge. + If the hyperedge does not exist, returns an empty frozenset. - if hyperedge_size is not None: - res = 0 - for s in star: - nodes = self.get_hyperedge_nodes(s) - if len(nodes) == hyperedge_size: - res += 1 - return res - else: - return len(star) + :param hyperedge_id: ID of the hyperedge. + :return: A frozenset of node IDs that are part of the hyperedge. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedge([1, 2], start=0) + H.get_hyperedge_nodes('e1') # frozenset({1, 2}) - def get_degree_by_hyperedge_size(self, node: int, tid: int = None) -> dict: """ - Given a node, the get_degree_by_hyperedge_size function returns a dictionary where keys are the sizes - of the hyperedges in the node's star, and values are the raw frequency of that size in the star. - For example, if there are two hyperedges with three nodes each and one - hyperedge with four nodes, then the returned dictionary would be: {3: 2, 4: 1}. - The optional parameter tid restricts the hyperedges to those active in that point in time. + return self._eid2nids.get(hyperedge_id, frozenset()) - :param node: Specify the node for which we want to calculate the degree distribution - :param tid: Specify a temporal snapshot - :return: A dictionary where the keys are the node's star's hyperedge sizes and the values are their frequencies + def get_hyperedge_id(self, nodes: Iterable[int]) -> str: """ + Get the hyperedge ID for a given set of node IDs. + If the hyperedge does not exist, raises a KeyError. + + :param nodes: Iterable of node IDs that form the hyperedge. + :return: The ID of the hyperedge as a string. + :raises KeyError: If the hyperedge does not exist. + + Examples + -------- + .. code-block:: python - distr = defaultdict(int) - star = self.get_star(node, tid=tid) - for s in star: - nodes = self.get_hyperedge_nodes(s) - distr[len(nodes)] += 1 - return distr + H = ASH() + H.add_hyperedge([1, 2], start=0) + eid = H.get_hyperedge_id([1, 2]) # 'e1' - def get_s_degree(self, node: int, s: int, tid: int = None) -> int: """ - The get_s_degree function returns the s-degree of a specific node. + return self._nids2eid[frozenset(nodes)] + # ------------------------------------------------------------------ + # Node & Hyperedge attributes + # ------------------------------------------------------------------ - :param node: Specify the node for which to compute the degree - :param s: Specify the minimum number of nodes in each hyperedge to be counted - :param tid: Temporal id - :return: The number of hyperedgess in the start that have at least s nodes + def get_node_profiles_by_time(self, node: int) -> Dict[int, NProfile]: """ + Get the profiles of a node at all available time instants. - degs = self.get_degree_by_hyperedge_size(node, tid) - res = 0 - for k, v in degs.items(): - if k >= s: - res += v - return res + :param node: Node ID for which to get the profiles. + :return: A dictionary mapping time IDs to NProfile instances. + + Examples + -------- + .. code-block:: python + + from ash_model.classes.node_profile import NProfile + + H = ASH() + H.add_node(1, 0, attr_dict=NProfile(1, role='A')) + H.add_node(1, 1, attr_dict=NProfile(1, role='B')) + profiles = H.get_node_profiles_by_time(1) + list(profiles.keys()) # [0, 1] - def has_node(self, node: int, tid: int = None) -> bool: """ - The has_node function checks if a node is present in the ASH. - Optionally, it is possible to check for presence at a specific point in time. + return { + tid: self.get_node_profile(node, tid) + for tid in self.node_presence(node, as_intervals=False) + } - :param node: The node whose presence is to be assessed - :param tid: Check if a node is present in the ASH at a specific time - :return: True if the node is present and False otherwise + def get_node_profile(self, node: int, tid: Optional[int] = None) -> NProfile: """ + Get the profile of a node. + The profile contains the node's attributes at a specific time ID. + If `tid` is None, the profile will be aggregated across all time IDs. - presence = self.H.has_node(node) - if presence and tid is not None: - attrs = self.get_node_profile(node) - if isinstance(attrs, NProfile): - attrs = attrs.get_attribute("t") - else: - attrs = attrs["t"] - for span in attrs: - if span[0] <= tid <= span[1]: - return True - return False - return presence + :param node: Node ID for which to get the profile. + :param tid: Time ID to filter the profile. If None, all time IDs are considered. + :return: An NProfile instance containing the node's attributes. - def node_iterator(self, tid: int = None) -> list: - """ - The node_iterator function returns an iterator over the nodes in the ASH. - If no temporal id (tid) is specified, it will iterate over all nodes. - Otherwise, it will iterate only over those nodes that exist at that temporal id. + Examples + -------- + .. code-block:: python + + from ash_model.classes.node_profile import NProfile + + H = ASH() + H.add_node(1, 0, attr_dict=NProfile(1, team='X')) + p0 = H.get_node_profile(1, 0) + p_all = H.get_node_profile(1) # aggregated profile - :param tid: Specify the temporal snapshot id - :return: An iterator over the ASH's nodes """ + from ash_model.utils import aggregate_node_profile if tid is None: - return self.H.node_iterator() - S, _ = self.hypergraph_temporal_slice(tid) - return S.H.node_iterator() + return aggregate_node_profile(self, node) + return NProfile(node, **dict(self._node_attrs[node][tid])) # type: ignore[arg-type] - def get_node_presence(self, node: int) -> list: + def get_node_attribute( + self, + node: int, + attr_name: str, + tid: Optional[int] = None, + ) -> Union[Any, Dict[int, Any]]: """ - The get_node_presence function returns a list of all the snapshots in which the node is present. - The function takes as input a node id and returns a list of all the snapshots in which that node is present. + Get a specific attribute of a node at a given time. + If `tid` is None, a dictionary mapping time IDs to attribute values is returned. + + :param node: Node ID for which to get the attribute. + :param attr_name: Name of the attribute to retrieve. + :param tid: Time ID to filter the attribute. If None, all time IDs are considered. + :return: The value of the attribute for the node at the specified time, or a dictionary of values if `tid` is None. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, start=0, attr_dict={"label": "A"}) + H.get_node_attribute(1, "label", tid=0) # 'A' + H.get_node_attribute(1, "label") # {0: 'A'} - :param node: Specify the node for which we want to get the presence - :return: A list of all the snapshots that a node is present in """ - snaps = [] - tids = self.get_node_attribute(node, "t") - for spans in tids.values(): - for span in spans: - snaps.extend(range(span[0], span[1] + 1)) - snaps = sorted(list(set(snaps))) - return snaps + if tid is None: + return { + t: self._node_attrs[node][t].get(attr_name, None) + for t in self._node_attrs[node] + } + else: + return self.get_node_attributes(node, tid).get(attr_name, None) + + def get_node_attributes( + self, node: int, tid: Optional[int] = None + ) -> Dict[str, Any]: + """ + Get all attributes of a node at a given time. + If `tid` is None, returns attributes across all time IDs. + + :param node: Node ID for which to get the attributes. + :param tid: Time ID to filter the attributes. If None, all time IDs are considered. + :return: A dictionary of attributes for the node at the specified time, or across all times if `tid` is None. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, 0, attr_dict={"x": 10}) + H.get_node_attributes(1, 0) # {'x': 10} + H.get_node_attributes(1) # {0: {'x': 10}} - def coverage(self) -> float: """ - The coverage function is the fraction of nodes in the ASH that are - present in at least one snapshot over all possible nodes and snapshots. - This measure is used to quantify how well the ASH has been preserved over time. - :return: The fraction of the nodes in the graph that are covered by at least one snapshot + if tid is None: + return dict(self._node_attrs[node]) if node in self._node_attrs else {} + else: + return ( + dict(self._node_attrs[node][tid]) + if tid in self._node_attrs[node] + else {} + ) + + def list_node_attributes( + self, categorical: bool = False, tid: Optional[int] = None + ) -> Dict[str, Set[Any]]: """ + List all attributes of nodes in the ASH, optionally filtered by time. + If `tid` is None, all attributes across all times are considered. + + :param categorical: If True, only categorical attributes (strings) are returned. + :param tid: Time ID to filter the attributes. If None, all time IDs are considered. + :return: A dictionary where keys are attribute names and values are sets of attribute values. - T = len(self.snapshots) - V = self.get_number_of_nodes() - W = 0 - for tid in self.snapshots: - W += self.get_number_of_nodes(tid) + Examples + -------- + .. code-block:: python - return W / (T * V) + H = ASH() + H.add_node(1, 0, attr_dict={"label": "A", "age": 30}) + H.add_node(2, 0, attr_dict={"label": "B"}) + all_attrs = H.list_node_attributes() + cat_attrs = H.list_node_attributes(categorical=True) - def node_contribution(self, node) -> float: """ - The node_contribution function returns the fraction of snapshots where the node is present. - This is used to determine how important a node is within the ASH. + attributes: DefaultDict[str, Set[Any]] = defaultdict(set) + if tid is None: + for node in self.nodes(): + for attr_dict in self._node_attrs[node].values(): + for attr, value in attr_dict.items(): + attributes[attr].add(value) + else: + for node in self.nodes(tid): + for attr, value in self._node_attrs[node][tid].items(): + attributes[attr].add(value) - :param node: Specify the node for which we want to calculate the contribution - :return: The contribution of a node to the overall coverage + if categorical: + attributes = defaultdict( + set, + {k: v for k, v in attributes.items() if isinstance(next(iter(v)), str)}, + ) + return dict(attributes) + + def get_hyperedge_attribute(self, hyperedge_id: str, attribute_name: str) -> Any: """ + Get a specific attribute of a hyperedge. + + :param hyperedge_id: ID of the hyperedge. + :param attribute_name: Name of the attribute to retrieve. + :return: The value of the attribute for the hyperedge, or None if not set + + Examples + -------- + .. code-block:: python - ucov = 0 - for tid in self.snapshots: - ucov += 1 if self.has_node(node, tid) else 0 - return ucov / len(self.snapshots) + H = ASH() + H.add_hyperedge([1, 2], start=0, weight=5) + H.get_hyperedge_attribute('e1', 'weight') # 5 - def node_degree_distribution(self, start: int = None, end: int = None) -> dict: """ - The node_degree_distribution function returns a dictionary of the number of nodes with each degree. - The function takes two optional arguments, start and end. If start is not specified, then it will return - the distribution for all nodes in the ASH. If only start is specified, then it will return the - distribution for all nodes from that point in time onwards. If both are specified, then it will return - the distribution for all nodes in that temporal slice range (tid>=start & tid<end). - The function returns a dictionary where keys are degrees and values are counts. + if hyperedge_id not in self._edge_attributes: + return None + if attribute_name not in self._edge_attributes[hyperedge_id]: + return None + return self._edge_attributes[hyperedge_id][attribute_name] - :param start: Starting point of optional time window - :param end: Ending point of optional time window - :return: A degree-to-frequency dictionary. + def get_hyperedge_attributes( + self, hyperedge_id: Optional[str] = None + ) -> Dict[str, Any]: """ - dist = defaultdict(int) + Get all attributes of a hyperedge. + If `hyperedge_id` is None, returns attributes for all hyperedges. + If the hyperedge does not exist, returns an empty dictionary. - if start is None: - for node in self.node_iterator(): - dist[self.get_degree(node)] += 1 + :param hyperedge_id: ID of the hyperedge. If None, all hyperedges are considered. - elif start is not None and end is None: - for node in self.node_iterator(tid=start): - dist[self.get_degree(node, tid=start)] += 1 + :return: A dictionary of attributes for the hyperedge, or an empty dictionary if not found. - else: - S, old_to_new = self.hypergraph_temporal_slice(start=start, end=end) - for node in S.node_iterator(): - dist[S.get_degree(node)] += 1 + Examples + -------- + .. code-block:: python - return dist + H = ASH() + H.add_hyperedges([[1, 2], [2, 3]], start=0, weight=1) + attrs_all = H.get_hyperedge_attributes() + attrs_e1 = H.get_hyperedge_attributes('e1') - ## Hyperedges + """ + if hyperedge_id is None: + return {he: attrs for he, attrs in self._edge_attributes.items()} + return dict(self._edge_attributes[hyperedge_id]) - def add_hyperedge(self, nodes: list, start: int, end: int = None, **attrs) -> None: + def list_hyperedge_attributes( + self, categorical: bool = False + ) -> Dict[str, Set[Any]]: """ - The add_hyperedge function adds a hyperedge to the ASH, active between :start: and :end:. - If the :end: parameter is not specified, it defaults to :start: + List all attributes of hyperedges in the ASH. + If `categorical` is True, only categorical attributes (strings) are returned. + + :param categorical: If True, only categorical attributes (strings) are returned. + :return: A dictionary where keys are attribute names and values are sets of attribute values. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedge([1, 2], start=0, color='blue') + H.list_hyperedge_attributes() # {'weight': {1}, 'color': {'blue'}} - :param nodes: Specify the nodes that are part of the hyperedge - :param start: Indicate the appearance time of the hyperedge - :param end: Indicate the vanishing time of the hyperedge - :param **attrs: Pass additional information about the interaction - :return: """ - if start is None: - raise ValueError("The hyperedge appearance time, t, cannot be None") - if end is not None and end < start: - raise ValueError( - "The vanishing time, e, (if present) must be equal or greater than the appearance one." + + attributes: DefaultDict[str, Set[Any]] = defaultdict(set) + + for hedge in self.hyperedges(): + for attr, value in self._edge_attributes[hedge].items(): + attributes[attr].add(value) + + if categorical: + attributes = defaultdict( + set, + {k: v for k, v in attributes.items() if isinstance(next(iter(v)), str)}, ) + return dict(attributes) - for u in nodes: - if not self.H.has_node(u): - self.add_node(u, start, end, {}) + def get_hyperedge_weight(self, hyperedge_id: str) -> Union[int, float]: + """ + Get the weight of a hyperedge. + If the weight is not set, returns 1 by default. - if end is None: - start = [start, start] - else: - start = [start, end] - - # add the interaction - if not self.H.has_hyperedge(nodes): # new hyperedge - presence = {"t": [start]} # : attr_dict}} - for k, v in attrs.items(): - presence[k] = v - - self.H.add_hyperedge(nodes, attr_dict=presence) - - else: # update existing one - eid = self.H.get_hyperedge_id(nodes) - old_attr = self.H.get_hyperedge_attributes(eid) - presence = old_attr["t"] - presence.append(start) - presence = sorted(presence) - - # compacting intervals - intervals = [] - for i, span in enumerate(presence): - if i < len(presence) - 1: - if span[1] == presence[i + 1][0] - 1: - intervals.append([span[0], presence[i + 1][1]]) - else: - intervals.append(span) - else: - intervals.append(span) + :param hyperedge_id: ID of the hyperedge. + :return: The weight of the hyperedge, or 1 if not set. - merged = self.__recursive_merge(intervals.copy()) + Examples + -------- + .. code-block:: python - # contiguity - cont = [merged[0]] - pos = 0 - for i in range(1, len(merged)): - if cont[pos][1] == merged[i][0]: - cont[pos][1] = merged[i][1] - else: - pos += 1 - cont.append(merged[i]) - - old_attr["t"] = cont - - old_attr["weight"] = len(merged) - self.H.add_hyperedge(nodes, old_attr) - - # lookup table (to do) - eid = self.H.get_hyperedge_id(nodes) - intervals = self.H.get_hyperedge_attributes(eid)["t"] - for span in intervals: - for i in range(span[0], span[1] + 1): - if eid in self.time_to_edge[i]: - del self.time_to_edge[i][eid] - self.time_to_edge[span[0]][eid] = "+" - if self.hedge_removal: - self.time_to_edge[span[1] + 1][eid] = "-" - - for x in range(start[0], start[1] + 1): - if x not in self.snapshots: - self.snapshots[x] = [eid] - else: - self.snapshots[x].append(eid) - self.snapshots[x] = list(set(self.snapshots[x])) + H = ASH() + H.add_hyperedge([1, 2], start=0) + H.get_hyperedge_weight('e1') # 1 - def add_hyperedges(self, hyperedges: list, start: int, end: int = None) -> None: """ - The add_hyperedges function adds a list of hyperedges to the ASH, all with the same start and end - snapshot ids. + weight = self.get_hyperedge_attribute(hyperedge_id, "weight") + return 1 if weight is None else weight + + # ------------------------------------------------------------------ + # Statistics + # ------------------------------------------------------------------ - :param hyperedges: Specify a list of lists of nodes representing hyperedges - :param start: Specify the starting temporal snapshot of the hyperedges - :param end: Specify the ending temporal snapshot of the hyperedges - :return: + def number_of_nodes( + self, start: Optional[int] = None, end: Optional[int] = None + ) -> int: """ + Return the number of unique nodes present in the ASH within the specified time window. + + :param start: Start time of the query. If None, all nodes are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: The number of unique nodes. - for nodes in hyperedges: - self.add_hyperedge(nodes, start, end) + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.number_of_nodes(0) # 3 - def get_hyperedge_attribute( - self, hyperedge_id: str, attribute_name: str, tid: int = None - ) -> object: """ - The get_hyperedge_attribute function returns the value of a specific attribute of a hyperedge. - :param hyperedge_id:str: Specify the hyperedge to get the attribute of - :param attribute_name: Specify the attribute that is to be returned - :param tid: Specify a time slot - :return: The attribute of a hyperedge + return len(self.nodes(start, end)) + + def number_of_hyperedges( + self, start: Optional[int] = None, end: Optional[int] = None + ) -> int: """ + Return the number of unique hyperedges present in the ASH within the specified time window. - # to check against attributes (not implemented) - attrs = self.H.get_hyperedge_attribute(hyperedge_id, attribute_name) + :param start: Start time of the query. If None, all hyperedges are considered + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: The number of unique hyperedges. - if tid is not None: - res = {} - for key, v in attrs.items(): - if key != "t" and key == attribute_name: - res[key] = v - else: - for span in v: - if span[0] <= tid <= span[1]: - res["t"] = [span] - if "t" in res: - return res - else: - raise ValueError("Hyperedge not present in the selected timeslot") - else: - return attrs + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedges([[1, 2], [2, 3]], start=0) + H.number_of_hyperedges(0) # 2 - def get_hyperedge_attributes(self, hyperedge_id: str, tid: int = None) -> dict: """ - The get_hyperedge_attributes function returns a dictionary of the attributes associated with a hyperedge. - If tid is specified, it will only return the attribute values for that timeslot. + return self.size(start, end) - :param hyperedge_id: Specify the hyperedge to get the attributes of - :param tid: Specify a snapshot - :return: The attributes of a hyperedge + def size(self, start: Optional[int] = None, end: Optional[int] = None) -> int: """ + Return the number of hyperedges present in the ASH within the specified time window. - attrs = self.H.get_hyperedge_attributes(hyperedge_id) - if tid is not None: - res = {} - for key, v in attrs.items(): - if key != "t": - res[key] = v - else: - for span in v: - if span[0] <= tid <= span[1]: - res["t"] = [span] - if "t" in res: - return res - else: - raise ValueError("Hyperedge not present in the selected timeslot") - else: - return attrs + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: The number of hyperedges. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedge([1, 2], start=0) + H.size(0) # 1 - def get_hyperedge_id(self, nodes: list) -> str: """ - The get_hyperedge_id function takes a list of nodes and returns the hyperedge ID - of the hyperedge that contains those nodes. - :param nodes: Specify the nodes that are in the hyperedge - :return: The id of the hyperedge that is formed by the nodes in the list + return len(self.hyperedges(start, end)) + + def hyperedge_size_distribution( + self, start: Optional[int] = None, end: Optional[int] = None + ) -> Dict[int, int]: """ + Return the distribution of hyperedge sizes within the specified time window. + The keys are the sizes of hyperedges (number of nodes in each hyperedge), + and the values are the counts of hyperedges of that size. + + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: A dictionary where keys are hyperedge sizes and values are counts of hyperedges of that size. - return self.H.get_hyperedge_id(nodes) + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedges([[1, 2], [2, 3, 4]], start=0) + H.hyperedge_size_distribution(0) # {2: 1, 3: 1} - def get_hyperedge_id_set(self, hyperedge_size: int = None, tid: int = None) -> set: """ - The get_hyperedge_id_set function returns the set of hyperedge IDs that satisfy the given constraints. The - function takes two optional arguments, hyperedge_size and tid. If no arguments are passed in, it will return - all hyperedges id in the ASH. If only hyperedge_size is passed in, it will return all hyperedges with size - equal to hyperedge_size. Finally, if both are specified, both constraint are respected. - :param hyperedge_size: Specify the size of hyperedges to be included - :param tid: Specify the snapshot of the hyperedges to consider - :return: A set of hyperedge ids that satisfy the given conditions + distr: DefaultDict[int, int] = defaultdict(int) + for he in self.hyperedges(start, end): + distr[len(self.get_hyperedge_nodes(he))] += 1 + return dict(distr) + + def degree_distribution( + self, start: Optional[int] = None, end: Optional[int] = None + ) -> Dict[int, int]: """ + Return the distribution of node degrees within the specified time window. + The keys are the degrees of nodes (number of hyperedges each node is part of), + and the values are the counts of nodes with that degree. - if tid is None: - if hyperedge_size is None: - return self.H.get_hyperedge_id_set() - else: - return { - he - for he in self.H.get_hyperedge_id_set() - if len(self.get_hyperedge_nodes(he)) == hyperedge_size - } - else: - hedges = {} - for i in range(min(self.time_to_edge.keys()), tid + 1): - hest = self.time_to_edge[i] - for key, v in hest.items(): - if v == "+" and ( - hyperedge_size is None - or len(self.get_hyperedge_nodes(key)) == hyperedge_size - ): - hedges[key] = None - else: - if key in hedges: - del hedges[key] - return set(hedges.keys()) + :param start: Start time of the query. If None, all nodes are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: A dictionary where keys are node degrees and values are counts of nodes with that degree. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [2, 3]], start=0) + H.degree_distribution(0) # e.g., {1: 2, 2: 1} - def get_hyperedge_nodes(self, hyperedge_id: str) -> list: """ - The get_hyperedge_nodes function returns a set of the nodes that are connected by the hyperedge with id - hyperedge_id. - :param hyperedge_id: Specify which hyperedge to get the nodes for - :return: The nodes that are connected by the hyperedge_id + distr: DefaultDict[int, int] = defaultdict(int) + for node in self.nodes(start, end): + distr[self.degree(node, start, end)] += 1 + return dict(distr) + + # ------------------------------------------------------------------ + # Node-centric analysis + # ------------------------------------------------------------------ + + def star( + self, + node: int, + start: Optional[int] = None, + end: Optional[int] = None, + hyperedge_size: Optional[int] = None, + as_ids: bool = True, + ) -> List[Union[str, frozenset[int]]]: """ + Return the star of a node, which is the set of hyperedges that contain the node + within the specified time window. If `hyperedge_size` is specified, only hyperedges + of that size are returned. The `as_ids` parameter determines whether to return hyperedge + IDs (strings) or sets of node IDs (frozensets). + + :param node: Node ID for which to get the star. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :param hyperedge_size: If specified, only hyperedges of this size are returned. + :param as_ids: If True, return hyperedge IDs; if False, return sets of node IDs. - return self.H.get_hyperedge_nodes(hyperedge_id) + :return: A list of hyperedge IDs or sets of node IDs that form the star of the node within the specified time window. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [1, 3]], start=0) + H.star(1, 0) # e.g., ['e1', 'e2'] + H.star(1, 0, as_ids=False) # [frozenset({1,2}), frozenset({1,3})] - def get_hyperedge_weight(self, hyperedge_id: str) -> int: """ - The get_hyperedge_weight function returns the weight of a hyperedge. - :param hyperedge_id: Identify the hyperedge - :return: The weight of the hyperedge with id hyperedge_id + if start is None: + star_set: Set[str] = set(self._stars[node]) + else: + star_set = set() + for t in self.__time_window(start, end): + star_set.update(self._stars[node].intersection(self._snapshots[t])) + + if hyperedge_size is not None: + star_set = { + s + for s in star_set + if len(self.get_hyperedge_nodes(s)) == hyperedge_size + } + + if as_ids: + return list(star_set) + return [self.get_hyperedge_nodes(s) for s in star_set] + + def degree( + self, + node: int, + start: Optional[int] = None, + end: Optional[int] = None, + hyperedge_size: Optional[int] = None, + ) -> int: """ + Return the degree of a node, which is the number of hyperedges that contain the node + within the specified time window. If `hyperedge_size` is specified, only hyperedges + of that size are counted. + + :param node: Node ID for which to get the degree. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :param hyperedge_size: If specified, only hyperedges of this size are counted. + + :return: The degree of the node within the specified time window. + + Examples + -------- + .. code-block:: python - return self.H.get_hyperedge_weight(hyperedge_id) + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [1, 3]], start=0) + H.degree(1, 0) # 2 - def has_hyperedge(self, nodes: list, tid: int = None) -> bool: """ - The has_hyperedge function checks to see if the ASH contains an hyperedge - formed by a specific set of nodes. Optionally, it checks at a specific snapshot (tid). - :param nodes: Specify the nodes that are part of the hyperedge - :param tid: To check whether the hyperedge exists in a specific snapshot - :return: True if the hyperedge with the given nodes exists, False otherwise + return len(self.star(node, start, end, hyperedge_size, as_ids=False)) + + def s_degree( + self, node: int, s: int, start: Optional[int] = None, end: Optional[int] = None + ) -> int: """ + Compute the s-degree of a node, summing degrees for hyperedges of size at least s. + + :param node: Node ID. + :param s: Minimum hyperedge size to consider. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :return: The s-degree value. - presence = self.H.has_hyperedge(nodes) - if presence and tid is not None: - eid = self.get_hyperedge_id(nodes) - return self.has_hyperedge_id(eid, tid) - return presence + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3, 4], start=0) + H.add_hyperedges([[1, 2], [1, 2, 3], [1, 3, 4]], start=0) + H.s_degree(1, s=3, start=0) # counts only size >= 3 -> 2 - def has_hyperedge_id(self, hyperedge_id: str, tid: int = None) -> bool: """ - The has_hyperedge_id function checks whether a hyperedge with id hyperedge_id is present in the ASH. - Optionally, it checks at a specific snapshot id (tid). + degs = self.degree_by_hyperedge_size(node, start, end) + return sum(v for k, v in degs.items() if k >= s) - :param hyperedge_id: Specify the hyperedge to be checked - :param tid: Optionally check if it exists at a specific snapshot - :return: A boolean indicating whether the hyperedge is present in the given snapshot + def degree_by_hyperedge_size( + self, node: int, start: Optional[int] = None, end: Optional[int] = None + ) -> Dict[int, int]: """ + Return the degree of a node by hyperedge size, which is a dictionary where keys are + hyperedge sizes (number of nodes in each hyperedge) and values are the counts of + hyperedges of that size that contain the node within the specified time window. + + :param node: Node ID for which to get the degree by hyperedge size. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. - presence = self.H.has_hyperedge_id(hyperedge_id) - if presence and tid is not None: - attrs = self.get_hyperedge_attributes(hyperedge_id)["t"] - for span in attrs: - if span[0] <= tid <= span[1]: - return True - return False - return presence + :return: A dictionary where keys are hyperedge sizes and values are counts of hyperedges of that size that contain the node within the specified time window. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [1, 2, 3]], start=0) + H.degree_by_hyperedge_size(1, 0) # {2: 1, 3: 1} - def hyperedge_id_iterator(self, start: int = None, end: int = None) -> list: """ - The hyperedge_id_iterator function returns a list of hyperedge IDs that are present in the ASH - between two points in time. If no start or end is specified, it will return all hyperedge IDs. - :param start: Indicate the start time of the temporal slice - :param end: Specify the end of the temporal slice - :return: A list of hyperedge ids that are in the temporal slice specified by start and end + distr: DefaultDict[int, int] = defaultdict(int) + for he in self.star(node, start, end, as_ids=False): + distr[len(he)] += 1 + return dict(distr) + + def neighbors( + self, + node: int, + start: Optional[int] = None, + end: Optional[int] = None, + hyperedge_size: Optional[int] = None, + ) -> Set[int]: """ + Return the set of neighbors of a node, which are the nodes that share hyperedges with + the specified node within the given time window. If `hyperedge_size` is specified, + only hyperedges of that size are considered for determining neighbors. - if start is None: - return self.H.hyperedge_id_iterator() - S, eid_to_new_eid = self.hypergraph_temporal_slice(start, end) - new_eid_to_old_eid = {v: k for k, v in eid_to_new_eid.items()} + :param node: Node ID for which to get the neighbors. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :param hyperedge_size: If specified, only hyperedges of this size are considered for determining neighbors. - edges = list(S.H.hyperedge_id_iterator()) - return [new_eid_to_old_eid[e] for e in edges] + :return: A set of node IDs that are neighbors of the specified node within the specified time window. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [1, 3]], start=0) + H.neighbors(1, 0) # {2, 3} - def get_size(self, tid: int = None) -> int: """ - The get_size function returns the number of hyperedges in an ASH. - If a temporal snapshot id (tid) is specified, it will count the hyperedges that are active in tid. - :param tid: Specify the temporal snapshot id - :return: The number of hyperedges in the ASH + neighbors: Set[int] = set() + for he in self.star(node, start, end, hyperedge_size, as_ids=False): + neighbors.update(he) + neighbors.discard(node) + return neighbors + + def number_of_neighbors( + self, + node: int, + start: Optional[int] = None, + end: Optional[int] = None, + hyperedge_size: Optional[int] = None, + ) -> int: """ + Return the number of unique neighbors of a node, which are the nodes that share hyperedges + with the specified node within the given time window. If `hyperedge_size` is specified + only hyperedges of that size are considered for determining neighbors. + + :param node: Node ID for which to get the number of neighbors. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + :param hyperedge_size: If specified, only hyperedges of this size are considered for determining neighbors. - return len(self.get_hyperedge_id_set(tid=tid)) + :return: The number of unique neighbors of the specified node within the specified time window. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_nodes([1, 2, 3], start=0) + H.add_hyperedges([[1, 2], [1, 3]], start=0) + H.number_of_neighbors(1, 0) # 2 - def get_avg_number_of_hyperedges(self) -> float: """ - The get_avg_number_of_hyperedges function returns the average number of - hyperedges in each snapshot. - :return: The average number of hyperedges per snapshot + return len(self.neighbors(node, start, end, hyperedge_size)) + + # ------------------------------------------------------------------ + # Transformations & projections + # ------------------------------------------------------------------ + + def bipartite_projection( + self, + start: Optional[int] = None, + end: Optional[int] = None, + keep_attrs: bool = False, + ) -> nx.Graph: """ + Create a bipartite projection of the ASH. - return sum([len(he) for he in self.snapshots.values()]) / len(self.snapshots) + :param start: Start time of the projection. If None, all hyperedges are considered. + :param end: End time of the projection (inclusive). If None, only the start time is considered. + :param keep_attrs: If True, keep node and hyperedge attributes in the projection. + + :return: A bipartite graph where nodes are hyperedges and nodes, and edges represent incidences between them. + + Examples + -------- + .. code-block:: python + + import networkx as nx + H = ASH() + H.add_hyperedge([1, 2], start=0) + G = H.bipartite_projection(0) + isinstance(G, nx.Graph) # True - def hyperedge_contribution(self, hyperedge_id: str) -> float: """ - The hyperedge_contribution function calculates the fraction of snapshots where - a given hyperedge is active. - :param hyperedge_id: Specify which hyperedge to calculate the contribution for - :return: The contribution of a hyperedge + from ash_model.utils import bipartite_projection + + return bipartite_projection(self, start, end, keep_attrs) + + def dual_hypergraph( + self, start: Optional[int] = None, end: Optional[int] = None + ) -> Tuple["ASH", Dict[str, str]]: """ + Create a dual hypergraph projection of the ASH. - attrs = self.get_hyperedge_attributes(hyperedge_id)["t"] - count = 0 - for span in attrs: - count += len(range(span[0], span[1] + 1)) - return count / len(self.snapshots) + :param start: Start time of the projection. If None, all hyperedges are considered. + :param end: End time of the projection (inclusive). If None, only the start time is considered. - # Slices + :return: A tuple containing the dual hypergraph and a mapping of original hyperedge IDs to new hyperedge IDs in the dual hypergraph. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedges([[1, 2], [2, 3]], start=0) + dual, mapping = H.dual_hypergraph(0) + isinstance(dual, ASH) # True - def hypergraph_temporal_slice(self, start: int, end: int = None) -> tuple: """ - The hypergraph_temporal_slice constructs a new ASH instance that contains hyperedges active in the given - time window. It returns both the new instance and a dictionary mapping old hyperedge ids to new hyperedge ids. - If no end time is specified, then all temporal ids greater or equal to start are considered. - :param start: Specify the start time of the temporal slice - :param end: Specify the end of the temporal slice - :return: an ASH instance and a dictionary mapping old hyperedge ids to new hyperedge ids + from ash_model.utils import dual_hypergraph_projection + + return dual_hypergraph_projection(self, start, end) + + def clique_projection( + self, + start: Optional[int] = None, + end: Optional[int] = None, + keep_attrs: bool = False, + ) -> nx.Graph: """ + Create a clique projection of the ASH. - if end is None and start in self.snapshots: - edges = set( - [ - e1 - for obs in range(min(self.snapshots), max(self.snapshots) + 1) - for e1 in self.snapshots.get(obs, []) - ] - ) + :param start: Start time of the projection. If None, all hyperedges are considered. + :param end: End time of the projection (inclusive). If None, only the start time is considered. + :param keep_attrs: If True, keep node and hyperedge attributes in the projection. - elif end is None and start not in self.snapshots: - edges = [] - else: - edges = set( - [ - e1 - for obs in range(min(self.snapshots), end + 1) - for e1 in self.snapshots.get(obs, []) - ] - ) + :return: A graph where each hyperedge is decomposed into a clique. - S = ASH() - eid_to_new_eid = {} - for e1 in edges: - he = self.get_hyperedge_nodes(e1) - e_attrs = self.get_hyperedge_attributes(e1) - t1 = e_attrs["t"] - - for span in t1: - if end is not None: - if span[0] >= start and span[1] <= end: - S.add_hyperedge(he, span[0], span[1]) - new_eid = S.get_hyperedge_id(he) - eid_to_new_eid[e1] = new_eid - - elif end >= span[0] >= start and span[1] >= end: - S.add_hyperedge(he, start=span[0], end=end) - new_eid = S.get_hyperedge_id(he) - eid_to_new_eid[e1] = new_eid - - elif span[0] < start and span[1] >= end: - S.add_hyperedge(he, start, span[1]) - new_eid = S.get_hyperedge_id(he) - eid_to_new_eid[e1] = new_eid - - # else: - # S.add_hyperedge(he, start, end) - # new_eid = S.get_hyperedge_id(he) - # eid_to_new_eid[e1] = new_eid + Examples + -------- + .. code-block:: python - else: - if span[0] >= start or start <= span[1]: - if span[0] != span[1]: - S.add_hyperedge(he, span[0], span[1]) - new_eid = S.get_hyperedge_id(he) - eid_to_new_eid[e1] = new_eid - - else: - S.add_hyperedge(he, span[0]) - new_eid = S.get_hyperedge_id(he) - eid_to_new_eid[e1] = new_eid - - for n in self.get_node_set(): - attrs = self.get_node_profile(n) - if not isinstance(attrs, NProfile): - t1 = attrs["t"] - else: - t1 = attrs.get_attribute("t") + import networkx as nx + H = ASH() + H.add_hyperedge([1, 2, 3], start=0) + G = H.clique_projection(0) + isinstance(G, nx.Graph) # True + + """ - for span in t1: - if end is not None: - if span[0] >= start and span[1] <= end: - S.add_node(n, span[0], span[1], attr_dict=attrs) - elif end >= span[0] >= start and span[1] >= end: - S.add_node(n, span[0], end, attr_dict=attrs) - elif span[0] < start and span[1] >= end: - S.add_node(n, start, span[1], attr_dict=attrs) + from ash_model.utils import clique_projection - else: - if span[0] <= start <= span[1]: - if span[0] != span[1]: - S.add_node(n, span[0], span[1], attr_dict=attrs) + return clique_projection(self, start, end, keep_attrs=keep_attrs) - else: - S.add_node(n, span[0], attr_dict=attrs) + def s_line_graph( + self, s: int = 1, start: Optional[int] = None, end: Optional[int] = None + ) -> nx.Graph: + """ + Create a line graph projection of the ASH, where each hyperedge is represented as a + node, and edges represent shared nodes between hyperedges. - return S, eid_to_new_eid + :param s: Minimum size of hyperedges to consider in the projection. + :param start: Start time of the projection. If None, all hyperedges are considered. + :param end: End time of the projection (inclusive). If None, only the start time is considered. + + :return: A line graph where nodes represent hyperedges and edges represent shared nodes. + + Examples + -------- + .. code-block:: python + + import networkx as nx + H = ASH() + H.add_hyperedges([[1, 2], [2, 3]], start=0) + LG = H.s_line_graph(s=1, start=0) + isinstance(LG, nx.Graph) # True - def uniformity(self) -> float: """ - Temporal hypergraph uniformity - :return: uniformity value for the hypergraph + from ash_model.utils import line_graph_projection + + return line_graph_projection(self, s, start, end) + + # ------------------------------------------------------------------ + # Temporal analysis + # ------------------------------------------------------------------ + + def avg_number_of_nodes(self) -> float: """ - nds = self.get_node_set() - numerator, denominator = 0, 0 - for u, v in combinations(nds, 2): - for t in self.snapshots: - if self.has_node(u, t) and self.has_node(v, t): - numerator += 1 - if self.has_node(u, t) or self.has_node(v, t): - denominator += 1 - return numerator / denominator + Calculate the average number of nodes across all temporal snapshots. + + :return: The average number of nodes. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, 0) + H.add_node(2, 1) + avg = H.avg_number_of_nodes() # e.g., 1.0 - def hyperedge_size_distribution(self, start: int = None, end: int = None) -> dict: """ - The hyperedge_size_distribution function returns a dictionary of the number of hyperedges with a given size. - The function takes two optional arguments, start and end. If only start is provided, then it will return the - distribution of hyperedge sizes starting from (and including) that time step. If both start and end are - provided, then it will return the distribution between those two indices (inclusive). The default behavior is - to return the distribution over all time steps. + nodes_snapshots = [ + self.number_of_nodes(tid) for tid in self.temporal_snapshots_ids() + ] + return sum(nodes_snapshots) / len(nodes_snapshots) if nodes_snapshots else 0.0 - :param start: Specify the starting time of the temporal slice - :param end: Specify the ending time of the temporal slice - :return: A size_to_count dictionary that contains the number of hyperedges with a given size + def avg_number_of_hyperedges(self) -> float: """ + Calculate the average number of hyperedges across all temporal snapshots. - dist = defaultdict(int) + :return: The average number of hyperedges. - if start is None: - for he in self.get_hyperedge_id_set(): - dist[len(self.get_hyperedge_nodes(he))] += 1 + Examples + -------- + .. code-block:: python - elif start is not None and end is None: - for he in self.get_hyperedge_id_set(tid=start): - dist[len(self.get_hyperedge_nodes(he))] += 1 + H = ASH() + H.add_hyperedge([1, 2], 0) + H.add_hyperedge([2, 3], 1) + H.avg_number_of_hyperedges() # e.g., 1.0 - else: - for tid in range(start, end + 1): - for he in self.get_hyperedge_id_set(tid=tid): - dist[len(self.get_hyperedge_nodes(he))] += 1 + """ - return dist + hes_snapshots = [self.size(tid) for tid in self.temporal_snapshots_ids()] + return sum(hes_snapshots) / len(hes_snapshots) if hes_snapshots else 0.0 - def __str__(self) -> str: + def node_presence( + self, node: int, as_intervals: bool = False + ) -> List[Union[int, Tuple[int, int]]]: """ - String representation of the ASH + Get the presence of a node across all temporal snapshots. + If `as_intervals` is True, returns the presence as intervals (start, end + times). Otherwise, returns a list of time IDs where the node is present. - :return: - """ - return json.dumps(self.to_dict(), indent=2) + :param node: Node ID for which to get the presence. + :param as_intervals: If True, return presence as intervals; if False, return presence as a list of time IDs. + + :return: A list of time IDs or intervals where the node is present. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_node(1, start=0, end=2) + H.node_presence(1) # [0, 1, 2] + H.node_presence(1, True) # [(0, 2)] - def to_dict(self) -> dict: """ - The to_dict function returns a dictionary representation of the ASH. - The keys are "nodes" and "hedges". The nodes key points to a dictionary, - where the keys are node ids and values are dictionaries containing all attributes - of that node. The hedges key points to another dictionary, where the keys are hyperedge ids - and values contain dictionaries with all attributes of that hyperedge, including appearence/disappearence temporal ids.. + times = sorted(self._node_attrs[node].keys()) + return ( + self.__presence_to_intervals(times) if as_intervals else times # type: ignore[return-value] + ) - :return: A dictionary representation of the ASH + def hyperedge_presence( + self, hyperedge_id: str, as_intervals: bool = False + ) -> List[Union[int, Tuple[int, int]]]: """ + Get the presence of a hyperedge across all temporal snapshots. + If `as_intervals` is True, returns the presence as intervals (start, end + times). Otherwise, returns a list of time IDs where the hyperedge is present. - descr = {"nodes": {}, "hedges": {}} + :param hyperedge_id: ID of the hyperedge for which to get the presence. + :param as_intervals: If True, return presence as intervals; if False, return presence as a list of time IDs. - for hedge in self.hyperedge_id_iterator(): - e = self.get_hyperedge_attributes(hedge) - descr["hedges"][hedge] = e + :return: A list of time IDs or intervals where the hyperedge is present. - for node in self.node_iterator(): - npr = self.get_node_profile(node) - descr["nodes"][node] = npr.get_attributes() - return descr + Examples + -------- + .. code-block:: python - # Transform + H = ASH() + H.add_hyperedge([1, 2], start=0, end=2) + H.hyperedge_presence('e1') # [0, 1, 2] + H.hyperedge_presence('e1', True) # [(0, 2)] - def s_line_graph(self, s: int = 1, start: int = None, end: int = None) -> object: """ - The s_line_graph function returns the corresponding s-line graph. Each node in the s-line graph represents a - hyperedge with at least s nodes. Two s-line graph nodes are linked if their corresponding hyperedges - intersect in at least s nodes in the original hypergraph. - :param s: Specify the minimum intersection between hyperedges - :param start: Specify the start of a time window - :param end: Specify the end of the interval - :return: The s-line graph of the ASH + pres = [ + t + for t in self.temporal_snapshots_ids() + if self.has_hyperedge(hyperedge_id, t) + ] + return ( + self.__presence_to_intervals(pres) if as_intervals else pres # type: ignore[return-value] + ) + + def node_contribution(self, node: int) -> float: """ - node_to_edges = defaultdict(list) - for he in self.hyperedge_id_iterator(start=start, end=end): - nodes = self.get_hyperedge_nodes(he) - for node in nodes: - node_to_edges[node].append(he) + Calculate the contribution of a node to the ASH, defined as the fraction of temporal snapshots + in which the node is present. - g = nx.Graph() - edges = defaultdict(int) - for eds in node_to_edges.values(): - if len(eds) > 0: - for e in combinations(eds, 2): - e = sorted(e) - edges[tuple(e)] += 1 + :param node: Node ID for which to calculate the contribution. + :return: The contribution of the node as a float between 0 and 1. - for e, v in edges.items(): - if v >= s: - g.add_edge(e[0], e[1], w=v) + Examples + -------- + .. code-block:: python - return g + H = ASH() + # Node 1 present in 1 out of 2 snapshots + H.add_node(1, 0) + H.add_node(2, 1) + H.node_contribution(1) # 0.5 - def bipartite_projection(self, start: int = None, end: int = None) -> object: """ - The bipartite_projection function creates a bipartite graph representation of the ASH leveraging NetworkX. - The nodes of type 0 represent ASH nodes, while nodes of type 1 represent hyperedges. - A type-0-node is connected to a type-1-node if the corresponding node is contained in the - corresponding hyperedge. - Parameters start and end define an optional time window to consider only entities active during those - points in time. - The function returns this new graph object. - :param start: Specify the start of a time window - :param end: Specify the end of a time window - :return: A networkx graph object + total_snapshots = len(self.temporal_snapshots_ids()) + if total_snapshots == 0: + return 0.0 + return ( + sum(1 for tid in self.temporal_snapshots_ids() if self.has_node(node, tid)) + / total_snapshots + ) + + def hyperedge_contribution(self, hyperedge_id: str) -> float: """ + Calculate the contribution of a hyperedge to the ASH, defined as the fraction of temporal + snapshots in which the hyperedge is present. - g = nx.Graph() - for he in self.hyperedge_id_iterator(start=start, end=end): - g.add_node(he, bipartite=1) - nodes = self.get_hyperedge_nodes(he) - for node in nodes: - if not g.has_node(node): - g.add_node(node, bipartite=0) - g.add_edge(node, he) + :param hyperedge_id: ID of the hyperedge for which to calculate the contribution. + :return: The contribution of the hyperedge as a float between 0 and 1 + + Examples + -------- + .. code-block:: python - return g + H = ASH() + # Edge present in 1 out of 2 snapshots + H.add_hyperedge([1, 2], 0) + H.add_node(3, 1) + H.hyperedge_contribution('e1') # 0.5 - def dual_hypergraph(self, start: int = None, end: int = None) -> tuple: """ - The dual_hypergraph function takes a hypergraph and returns the dual of that hypergraph. - The dual of a hypergraph is a graph where each hyperedge becomes a node, and each - node is connected to every other node in its corresponding hyperedge. The function also - returns an edge_to_nodes dictionary which maps edges to their corresponding nodes. + total_snapshots = len(self.temporal_snapshots_ids()) + if total_snapshots == 0: + return 0.0 + return ( + sum( + 1 + for tid in self.temporal_snapshots_ids() + if self.has_hyperedge(hyperedge_id, tid) + ) + / total_snapshots + ) - :param start: Specify the start of a time window - :param end: SpSpecify the end of a time window - :return: the dual ASH and a node-to-edge mapping dictionary + def coverage(self) -> float: """ + Calculate the coverage of the ASH, defined as the average number of nodes present across all + temporal snapshots, normalized by the total number of nodes. - b = ASH(hedge_removal=True) - node_to_edges = defaultdict(list) - for he in self.hyperedge_id_iterator(start=start, end=end): - nodes = self.get_hyperedge_nodes(he) - for node in nodes: - node_to_edges[node].append(he) + :return: The coverage of the ASH as a float between 0 and 1 - node_to_eid = {} - for node, edges in node_to_edges.items(): - b.add_hyperedge(edges, 0, end=None, **{"name": node}) - eid = b.get_hyperedge_id(edges) - node_to_eid[node] = eid + Examples + -------- + .. code-block:: python - return b, node_to_eid + # Two snapshots, 2 nodes total; average present per snapshot = 1.0 -> coverage 0.5 + H = ASH() + H.add_node(1, 0) + H.add_node(2, 1) + H.coverage() # 0.5 - def adjacency(self, node_set: set, start: int = None, end: int = None) -> int: """ - :param node_set: - :param start: - :param end: - :return: + tids = self.temporal_snapshots_ids() + if not tids or self.number_of_nodes() == 0: + return 0.0 + w = sum(self.number_of_nodes(tid) for tid in tids) + return w / (len(tids) * self.number_of_nodes()) + + def uniformity(self) -> float: """ - count = 0 + Calculate the uniformity of the ASH, defined as the fraction of pairs of nodes that + are present together in at least one temporal snapshot, normalized by the total number of pairs. - for he in self.hyperedge_id_iterator(start=start, end=end): - nodes = self.get_hyperedge_nodes(he) - inc = set(nodes) & set(node_set) - if len(inc) == len(node_set): - count += 1 - return count + :return: The uniformity of the ASH as a float between 0 and 1 + + Examples + -------- + .. code-block:: python + + # Nodes (1,2) co-present at t=0; (1,3) never; (2,3) co-present at t=1 + H = ASH() + H.add_node(1, 0) + H.add_node(2, 0) + H.add_node(2, 1) + H.add_node(3, 1) + u = H.uniformity() # between 0 and 1 - def incidence(self, edge_set: set, start: int = None, end: int = None) -> int: """ - :param edge_set: - :param start: - :param end: - :return: + nds = self.nodes() + numerator, denominator = 0, 0 + for u, v in combinations(nds, 2): + for t in self.temporal_snapshots_ids(): + u_present = self.has_node(u, t) + v_present = self.has_node(v, t) + if u_present and v_present: + numerator += 1 + if u_present or v_present: + denominator += 1 + return numerator / denominator if denominator else 0.0 + + # ------------------------------------------------------------------ + # Slice & filter + # ------------------------------------------------------------------ + + def temporal_slice( + self, start: int, end: Optional[int] = None, keep_attrs: bool = True + ) -> Tuple["ASH", Dict[str, str]]: """ + Create a temporal slice of the ASH from `start` to `end` (inclusive). + If `end` is None, the slice will only include the time `start`. + The `keep_attrs` parameter determines whether to keep node attributes in the slice. + + :param start: Start time of the slice. + :param end: End time of the slice (inclusive). If None, the slice will only include the time `start`. + :param keep_attrs: If True, node attributes are preserved in the slice. + + :return: A tuple containing the new ASH and a mapping from old hyperedge IDs to new hyperedge IDs. + + Examples + -------- + .. code-block:: python - first = True + H = ASH() + H.add_hyperedge([1, 2], start=0) + H.add_hyperedge([2, 3], start=1) + sub, mapping = H.temporal_slice(0) + isinstance(sub, ASH) # True + + """ + + res = ASH() + eid_to_new_eid: Dict[str, str] = {} if end is None: end = start + for t in range(start, end + 1): + for hedge_id in self.hyperedges(t): + nodes = self.get_hyperedge_nodes(hedge_id) + res.add_hyperedge(nodes, t, t) + eid_to_new_eid[hedge_id] = res._nids2eid[frozenset(nodes)] + + if keep_attrs: + for t in range(start, end + 1): + for node in self.nodes(t): + profile = self.get_node_profile(node, t) + res.add_node(node, t, t, profile) + return res, eid_to_new_eid + + def induced_hypergraph( + self, hyperedge_set: Iterable[str], keep_attrs: bool = True + ) -> Tuple["ASH", Dict[str, str]]: + """ + Create an induced hypergraph from the ASH using a set of hyperedge IDs. + The `keep_attrs` parameter determines whether to keep node attributes in the new hypergraph. + + :param hyperedge_set: Iterable of hyperedge IDs to include in the induced hypergraph. + :param keep_attrs: If True, node attributes are preserved in the new hypergraph. + + :return: A tuple containing the new ASH and a mapping from old hyperedge IDs to new hyperedge IDs. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedges([[1, 2], [2, 3]], start=0) + sub, mapping = H.induced_hypergraph(['e1']) + set(sub.hyperedges()) # {'e1'} in subgraph namespace - res = set() - for he in edge_set: + """ + + b = ASH() + old_eid_to_new: Dict[str, str] = {} + + for he in hyperedge_set: + presence = self.hyperedge_presence(he, as_intervals=True) # type: ignore[arg-type] nodes = self.get_hyperedge_nodes(he) - filtered_nodes = [] - if start is None: - for node in nodes: - if self.has_node(node): - filtered_nodes.append(node) - filtered_nodes = list(set(filtered_nodes)) - else: - for tid in range(start, end + 1): - for node in nodes: - if self.has_node(node, tid): - filtered_nodes.append(node) - filtered_nodes = list(set(filtered_nodes)) - - if first: - first = False - res = set(filtered_nodes) - else: - res = set(filtered_nodes) & res + for span in presence: # type: ignore[assignment] + b.add_hyperedge(nodes, span[0], span[1]) # type: ignore[index] + new_he = b.get_hyperedge_id(nodes) + old_eid_to_new[he] = new_he + + if keep_attrs: + for t in b.temporal_snapshots_ids(): + for node in b.nodes(t): + profile = self.get_node_profile(node, t) + b.add_node(node, start=t, end=t, attr_dict=profile) - return len(res) + return b, old_eid_to_new def get_s_incident( - self, hyperedge_id: str, s: int, start: int = None, end: int = None - ) -> list: + self, + hyperedge_id: str, + s: int, + start: Optional[int] = None, + end: Optional[int] = None, + ) -> List[Tuple[str, int]]: """ - Returns a list of 2-tuples of the form (**heid**, **comm**), where heid is the id of a hyperedge that - intersects the input hyperedge by at least s nodes, and comm is the number of common nodes between the two - hyperedges. + Get hyperedges that are incident to a given hyperedge with at least `s` nodes + in common within the specified time window. Returns a list of tuples containing + hyperedge IDs and the number of nodes they share with the specified hyperedge. + + :param hyperedge_id: ID of the hyperedge to check against. + :param s: Minimum number of nodes that must be shared with the specified hyperedge. + :param start: Start time of the query. If None, all hyperedges are considered. + :param end: End time of the query (inclusive). If None, only the start time is considered. + + :return: A list of tuples where each tuple contains a hyperedge ID and the number of nodes it shares with the specified hyperedge. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedges([[1, 2, 3], [1, 3, 4], [4, 5]], start=0) + H.get_s_incident('e1', s=2, start=0) # [('e2', 2)] - :param hyperedge_id: Specify the hyperedge id - :param s: Specify the minimum number of common nodes - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :return: the list of s_incident hyperedges """ - res = [] + res: List[Tuple[str, int]] = [] nodes = set(self.get_hyperedge_nodes(hyperedge_id)) - for he in self.hyperedge_id_iterator(start=start, end=end): + hes = self.hyperedges(start, end) + for he in hes: if he != hyperedge_id: he_nodes = set(self.get_hyperedge_nodes(he)) incident = len(nodes & he_nodes) if incident >= s: res.append((he, incident)) - return res - def induced_hypergraph(self, hyperedge_set: list) -> object: + # ------------------------------------------------------------------ + # Serialization helpers + # ------------------------------------------------------------------ + + def to_dict(self) -> Dict[str, Any]: """ - The induced_hypergraph function takes a list of hyperedge IDs and returns the induced hypergraph. - The induced hypergraph is constructed by adding all nodes in the original graph that are included in any of - the hyperedges in the list. It also preserves temporal and attributive information. + Convert the ASH to a dictionary representation. + This includes nodes, hyperedges, and their attributes. + + :return: A dictionary representation of the ASH. + + Examples + -------- + .. code-block:: python + + H = ASH() + H.add_hyperedge([1, 2], start=0) + d = H.to_dict() + set(d.keys()) # {'nodes', 'hedges'} - :param hyperedge_set: Specify which hyperedges to induce - :return: A new ASH object and a dictionary that maps the old hyperedge ids to the new ones """ + return self.__dict__() - b = ASH() - nodes_to_add = {} - old_eid_to_new = {} - for he in self.hyperedge_id_iterator(): - if he in hyperedge_set: - att = self.get_hyperedge_attributes(he)["t"] - nodes = self.get_hyperedge_nodes(he) - for n in nodes: - nodes_to_add[n] = None - - for span in att: - b.add_hyperedge(self.get_hyperedge_nodes(he), span[0], span[1]) - he1 = b.get_hyperedge_id(nodes) - old_eid_to_new[he] = he1 - - for node in nodes_to_add: - prof = self.get_node_profile(node) - spans = prof.get_attribute("t") - for t in spans: - pt = self.get_node_profile(node, tid=t[0]) - b.add_node(node, t[0], t[1], attr_dict=pt) + def __dict__(self) -> Dict[str, Any]: - return b, old_eid_to_new + descr: Dict[str, Any] = {"nodes": {}, "hedges": {}} + + for hedge in self.hyperedges(): + edge_data: Dict[str, Any] = { + "nodes": list(self.get_hyperedge_nodes(hedge)), + "attributes": self.get_hyperedge_attributes(hedge), + } + edge_data["attributes"]["_presence"] = self.hyperedge_presence( + hedge, as_intervals=True # type: ignore[arg-type] + ) + descr["hedges"][hedge] = edge_data + + for node in self.nodes(): + descr["nodes"][node] = self.get_node_attributes(node) + + return descr + + # ------------------------------------------------------------------ + # String representation + # ------------------------------------------------------------------ + + def __str__(self) -> str: + descr = "Attributed Stream Hypergraph\n" + descr += f"Nodes: {self.number_of_nodes()}\n" + descr += f"Hyperedges: {self.number_of_hyperedges()}\n" + descr += f"Snapshots: {len(self.temporal_snapshots_ids())}\n" + descr += "Node attributes: " + ", ".join(self.list_node_attributes()) + "\n" + return descr diff --git a/ash_model/generators/__init__.py b/ash_model/generators/__init__.py new file mode 100644 index 0000000..400901e --- /dev/null +++ b/ash_model/generators/__init__.py @@ -0,0 +1,2 @@ +from .homophily_driven import * +from .random import * \ No newline at end of file diff --git a/ash_model/generators/homophily_driven.py b/ash_model/generators/homophily_driven.py new file mode 100644 index 0000000..44f62ab --- /dev/null +++ b/ash_model/generators/homophily_driven.py @@ -0,0 +1,148 @@ +import random +import numpy as np +from ash_model import ASH, NProfile + + +def _compute_probs_hba(h: ASH, node: int, homophily_rate: float) -> list: + target_prob_dict = {} + new_node_attr = h.get_node_attribute(node, attr_name="color", tid=0) + for n in range(node): + p = ( + homophily_rate + if new_node_attr == h.get_node_attribute(n, attr_name="color", tid=0) + else 1 - homophily_rate + ) + p *= h.degree(n, start=0) + 0.00001 # avoid division by 0 + target_prob_dict[n] = p + prob_sum = sum(target_prob_dict.values()) + return [v / prob_sum for _, v in target_prob_dict.items()] + + +def _random_hyperedge(n, probs, he_size): + if he_size < 2: + return + try: + new_hyperedge = list( + np.random.choice(range(n), size=he_size - 1, p=probs, replace=False) + ) + new_hyperedge.append(n) + return set(new_hyperedge) + except ValueError: + _random_hyperedge(n, probs, he_size - 1) + + +def _truncated_pareto( + alpha: float, + size: int, + xmin: float = 2.0, + xmax: float = 10.0, + rng: np.random.Generator = None, +) -> np.ndarray: + """ + Generates a truncated Pareto distribution. + + :param alpha: Shape parameter of the Pareto distribution. + :param size: Number of samples to generate. + :param xmin: Minimum value of the distribution. + :param xmax: Maximum value of the distribution. + :param rng: Optional random number generator. + :return: An array of samples from the truncated Pareto distribution. + + """ + if xmin <= 0: + raise ValueError("xmin must be positive.") + if xmax < xmin: + raise ValueError("xmax must be >= xmin.") + if alpha <= 0: + raise ValueError("alpha must be positive.") + + rng = rng or np.random.default_rng() + + # CDF of Pareto at xmax: F_max = 1 - (xmin / xmax)**alpha + F_max = 1.0 - (xmin / xmax) ** alpha + + # Draw uniform variables restricted to [0, F_max] + u = rng.random(size) + + # Inverse CDF for the truncated case + samples = xmin / (1.0 - u * F_max) ** (1.0 / alpha) + return samples + + +def _sample_to_prob_distr(sample): + """ + Converts a sample to a probability distribution. + + :param sample: A list of samples. + :return: A list of probabilities normalized to sum to 1. + + """ + total = sum(sample) + if total == 0: + return [1.0 / len(sample)] * len( + sample + ) # Uniform distribution if total is zero + return [x / total for x in sample] + + +def ba_with_homophily( + num_nodes, m, homophily_rate, minority_size, n0, size_prob_distr=None +): + """ + Generates a Barabasi-Albert hypergraph with homophily-driven connections. + + :param num_nodes: Total number of nodes in the hypergraph. + :param m: Number of edges to attach from a new node to existing nodes. + :param homophily_rate: Probability of connecting to nodes with the same attribute. + :param minority_size: Proportion of nodes with the minority attribute. + :param n0: Number of initial nodes to start the hypergraph. + :param size_prob_distr: Optional probability distribution for hyperedge sizes. + If None, a truncated Pareto distribution is used. + + :return: An ASH object representing the generated hypergraph. + :raises ValueError: If homophily_rate or minority_size is not in the range [0, 1]. + + """ + if not (0 <= homophily_rate <= 1): + raise ValueError("Homophily rate must be between 0 and 1.") + if not (0 <= minority_size <= 1): + raise ValueError("Minority size must be between 0 and 1.") + + h = ASH() + # if size_prob_distr is None sample from pareto distribution + if size_prob_distr is None: + size_prob_distr = _truncated_pareto( + alpha=1.5, + size=num_nodes * m * 2, + xmin=2.0, + xmax=10.0, + rng=np.random.default_rng(), + ) + size_prob_distr = _sample_to_prob_distr(size_prob_distr) + + for n in range(num_nodes): + if random.random() > minority_size: + attr = "red" + else: + attr = "blue" + p = NProfile(node_id=n, color=attr) + h.add_node(n, start=0, end=0, attr_dict=p) + if n < n0: + continue + + # add m new hyperedges of random sizes + new_hyperedges = set() + for _ in range(m): + he_size = np.random.choice( + range(2, len(size_prob_distr) + 2), p=size_prob_distr + ) + + probs = _compute_probs_hba( + h, n, homophily_rate + ) # based on node degree and homophily + new_hyperedge = _random_hyperedge(n, probs, he_size) + if new_hyperedge: # None in case n does not find another node to connect to + new_hyperedges.add(frozenset(new_hyperedge)) + + h.add_hyperedges(new_hyperedges, start=0, end=0) + return h diff --git a/ash_model/generators/random.py b/ash_model/generators/random.py new file mode 100644 index 0000000..ae61ed1 --- /dev/null +++ b/ash_model/generators/random.py @@ -0,0 +1,97 @@ +import random +from ash_model import ASH, NProfile + + +def random_hypergraph( + num_nodes: int, size_distr: dict, node_attrs: dict = None, seed=None +) -> ASH: + """ + Generates a random hypergraph with the specified number of nodes and size distribution. + + :param num_nodes: The number of nodes in the hypergraph. + :param size_distr: A dictionary where keys are hyperedge sizes and values are their probabilities. + :param seed: Optional seed for random number generation. + :return: An ASH object representing the generated hypergraph. + + """ + if seed is not None: + random.seed(seed) + + h = ASH() + + for i in range(num_nodes): + profile = NProfile( + node_id=i, + **( + {attr: random.choice(values) for attr, values in node_attrs.items()} + if node_attrs + else {} + ) + ) + h.add_node(i, start=0, end=0, attr_dict=profile) + + for size, count in size_distr.items(): + for _ in range(count): + # Randomly select nodes for the hyperedge + nodes = random.sample(range(num_nodes), size) + h.add_hyperedge(nodes, start=0, end=0) + + # Optionally, add node attributes + if node_attrs: + for i in range(num_nodes): + profile = NProfile( + id=i, + **{attr: random.choice(values) for attr, values in node_attrs.items()} + ) + + return h + + +def random_ash( + num_nodes: int, + size_distr: dict, + time_steps: int, + node_attrs: dict = None, + seed=None, +) -> ASH: + """ + Generates a random ASH (Attributed Simple Hypergraph) with the specified number of nodes, + size distribution, and time steps. + + :param num_nodes: The number of nodes in the ASH. + :param size_distr: A dictionary where keys are hyperedge sizes and values are their probabilities. + :param time_steps: The number of time steps for the ASH. + :param node_attrs: Optional dictionary of attribute-to-values + :param seed: Optional seed for random number generation. + :return: An ASH object representing the generated hypergraph. + + """ + if seed is not None: + random.seed(seed) + + G = ASH() + + # example node_attrs: {'color': ['red', 'blue', 'green'], 'age': [1, 2, 3]} + + # add nodes + for i in range(num_nodes): + profile = NProfile( + node_id=i, + start=0, + end=time_steps - 1, + **( + {attr: random.choice(values) for attr, values in node_attrs.items()} + if node_attrs + else {} + ) + ) + G.add_node(i, start=0, end=time_steps - 1, attr_dict=profile) + + for size, count in size_distr.items(): + for _ in range(count): + # Randomly select nodes for the hyperedge + nodes = random.sample(range(num_nodes), size) + # Add the hyperedge to the ASH + G.add_hyperedge(nodes, start=0, end=time_steps - 1) + + return G diff --git a/ash_model/measures/attribute_analysis.py b/ash_model/measures/attribute_analysis.py index 29ac835..b14a90d 100644 --- a/ash_model/measures/attribute_analysis.py +++ b/ash_model/measures/attribute_analysis.py @@ -1,10 +1,10 @@ from collections import defaultdict, Counter from math import log, e -from typing import Callable import numpy as np from ash_model import ASH, NProfile +from ash_model.utils import hyperedge_aggregate_node_profile def __entropy(labels, base=None): @@ -12,7 +12,9 @@ def __entropy(labels, base=None): :param labels: :param base: + :return: + """ n_labels = len(labels) @@ -37,186 +39,106 @@ def __entropy(labels, base=None): return ent -def hyperedge_most_frequent_node_attribute_value( - h: ASH, hyperedge_id: str, attribute: str, tid: int -) -> dict: - """ - The hyperedge_most_frequent_node_attribute_value function returns the most frequent value of a given attribute - for the nodes in a hyperedge. If there are multiple values with the same frequency, then only one is returned. - The function returns an empty dictionary if no node has that attribute. - - :param h: ASH instance - :param hyperedge_id: Specify the hyperedge of interest - :param attribute: Specify the attribute name - :param tid: Temporal snapshot id - :return: A dictionary containing the attribute value and its frequency in the hyperedge - +def __purity(labels): """ + purity is the relative frequency of the most common attribute value + this returns a dictionary mapping the most common value to its purity - nodes = h.get_hyperedge_nodes(hyperedge_id) - app = defaultdict(list) - for node in nodes: - profile = h.get_node_profile(node, tid=tid) - - if not profile.has_attribute(attribute): - continue - - value = profile.get_attribute(attribute) - - if isinstance(value, str): - app[attribute].append(value) - - if isinstance(value, dict): - vals = [v for v in value.values()] - app[attribute].extend(vals) - - count = Counter(app[attribute]) - - if len(count) > 0: - count = count.most_common(1)[0] - res = {count[0]: count[1]} - return res - return {} - + :param labels: -def hyperedge_aggregate_node_profile( - h: ASH, hyperedge_id: str, tid: int, agg_function: Callable[[list], float] = np.mean -) -> NProfile: - """ - The hyperedge_aggregate_node_profile function takes a hyperedge ID and an aggregation function, and returns the - aggregate profile of all nodes in that hyperedge. The resulting NProfile will have as statistic the standard - deviation of each attribute in the original nodes' profiles + :return: - :param h: ASH instance - :param hyperedge_id: Identify the hyperedge that we want to aggregate - :param tid: Temporal snapshot id - :param agg_function: Specify the aggregation function - :return: The aggregated node profile of the hyperedge nodes """ - nodes = h.get_hyperedge_nodes(hyperedge_id) - avg_profile = NProfile(None) - res = defaultdict(list) - for node in nodes: - profile = h.get_node_profile(node, tid=tid) - for key, value in profile.items(): - if not isinstance(value, str): - res[key].append(value) + res = {} # attr -> purity - for key, value in res.items(): - avg_profile.add_attribute(key, agg_function(value)) - avg_profile.add_statistic(key, "std", np.std(value)) - - return avg_profile + counter = Counter(labels).most_common(1)[0] + if len(counter) == 0: + return res + return {counter[0]: counter[1] / len(labels)} def hyperedge_profile_purity(h: ASH, hyperedge_id: str, tid: int) -> dict: """ - The hyperedge_profile_purity function returns a dictionary of dictionaries. - The outer dictionary is keyed by the attribute names, and each inner dictionary - is keyed by the values of that attribute. Each inner dictionary contains two keys: - 'count' and 'purity'. The count represents how many times that value was seen - in the hyperedge, while purity represents what percentage of nodes with that - value make up the hyperedge. + Computes the purity of the hyperedge profile, i.e., the relative frequency of the most common attribute value + for each attribute in the hyperedge nodes' profiles. + + :param h: The ASH object + :param hyperedge_id: The hyperedge id + :param tid: The temporal id + + :return: A dictionary with attribute names as keys and their purity as values + + Examples + -------- + Build a small temporal ASH from 10 Barabási–Albert graphs, annotate nodes with a categorical color, + then compute the purity on one hyperedge at tid=0. + + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> tid = 0 + >>> he0 = next(iter(h.hyperedges(start=tid, end=tid))) + >>> hyperedge_profile_purity(h, he0, tid) + {'color': {'blue': 1.0}} - :param h: ASH instance - :param hyperedge_id: Specify the hyperedge for which we want to compute the purity - :param tid: Temporal snapshot id - :return: A dictionary with the attribute names as keys and a dictionary of the most - frequent value for that attribute in the hyperedge as values """ nodes = h.get_hyperedge_nodes(hyperedge_id) attributes = set() + attr_values = defaultdict(list) for node in nodes: profile = h.get_node_profile(node, tid) prof = profile.get_attributes() names = prof.keys() - keys = [] for name in names: if isinstance(profile.get_attribute(name), str): - keys.append(name) - - if len(attributes) == 0: - attributes = set(keys) - else: - attributes = attributes & set(keys) + attributes.add(name) + attr_values[name].append(profile.get_attribute(name)) res = {} for attribute in attributes: - res[attribute] = hyperedge_most_frequent_node_attribute_value( - h, hyperedge_id, attribute, tid - ) - - for attr, data in res.items(): - for k, _ in data.items(): - data[k] /= len(nodes) - res[attr] = data + res[attribute] = __purity(attr_values[attribute]) # {most_common_class: purity} return res -def average_hyperedge_profile_purity( - h: ASH, tid: int, by_label: bool = True, min_hyperedge_size: int = 2 -) -> object: - """ - The average_hyperedge_profile_purity function calculates the average purity value for each node attribute. If - :by_label: is True, the average is computed for each attribute value. For instance, if the profiles have the - attribute 'party', which can take the values 'L' or 'R', two averages for 'party' will be computed: one over all - the hyperedges whose most frequent label is 'L', and one over all the hyperedges whose most frequent label is 'R'. - - Otherwise, the average purity is computed over all hyperedges. - - :param h: ASH instance - :param tid: Specify the temporal id - :param by_label: Determine if the purity is computed for each label or not - :param min_hyperedge_size: Set the minimum size of a hyperedge to be considered in the average :return: A - dictionary containing for each attribute, for each attribute value, the average purity. If :by_label: is False, - returns a dictionary mapping each attribute to the average purity over all hyperedges - """ - - attributes = h.node_attributes_to_attribute_values(categorical=True) - if by_label: - purities = { - attribute: { - attribute_value: [] for attribute_value in attributes[attribute] - } - for attribute in attributes - } - - else: - purities = {attribute: [] for attribute in attributes} - - for hyperedge_id in h.get_hyperedge_id_set(tid=tid): - if len(h.get_hyperedge_nodes(hyperedge_id)) >= min_hyperedge_size: - purity = hyperedge_profile_purity(h, hyperedge_id=hyperedge_id, tid=tid) - for attr_name, result in purity.items(): - label = list(result.keys())[0] - pur = list(result.values())[0] - if by_label: - purities[attr_name][label].append(pur) - else: - purities[attr_name].append(pur) - if by_label: - return { - attribute: {val: np.mean(res) for val, res in results.items()} - for attribute, results in purities.items() - } - return {k: np.mean(v) for k, v in purities.items()} - - def hyperedge_profile_entropy(h: ASH, hyperedge_id: str, tid: int) -> dict: """ - The hyperedge_profile_entropy function calculates the entropy of each node attribute in a hyperedge. + Computes the entropy of the hyperedge profile, i.e., the entropy of the attribute values + for each attribute in the hyperedge nodes' profiles. + + :param h: The ASH object + :param hyperedge_id: The hyperedge id + :param tid: The temporal id + + :return: A dictionary with attribute names as keys and their entropy as values + + Examples + -------- + Using the same dataset as above, the entropy for the selected hyperedge at tid=0: + + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> tid = 0 + >>> he0 = next(iter(h.hyperedges(start=tid, end=tid))) + >>> hyperedge_profile_entropy(h, he0, tid) + {'color': 0} - :param h: ASH instance - :param hyperedge_id: Specify the hyperedge for which the entropy is calculated - :param tid: Temporal snapshot id - :return: A dictionary with the entropy of each attribute of the hyperedge's nodes """ - nodes = h.get_hyperedge_nodes(hyperedge_id) attributes = defaultdict(list) @@ -237,60 +159,53 @@ def hyperedge_profile_entropy(h: ASH, hyperedge_id: str, tid: int) -> dict: return res -def average_hyperedge_profile_entropy(h: ASH, tid: int) -> dict: - """ - Computes the average hyperedge profile entropy over all hyperedges in the ASH. For all attributes. - - :param h: ASH instance - :param tid: Temporal snapshot id - :return: A dictionary mapping each node attribute to the average entropy value - """ - entropies = defaultdict(list) - for hyperedge_id in h.get_hyperedge_id_set(tid=tid): - ent = hyperedge_profile_entropy(h, hyperedge_id, tid=tid) - for attr_name, val in ent.items(): - entropies[attr_name].append(val) - - return {k: np.mean(v) for k, v in entropies.items()} - - def star_profile_entropy( h: ASH, node_id: int, tid: int, method: str = "aggregate" ) -> dict: """ - The star_profile_entropy function computes the entropy of each attribute in the star of a given node. - If 'aggregate', it is computed by first aggregating the hyperedges into a single profile. - If 'collapse', all the star nodes are considered. + Returns the entropy of the star profile of a node, i.e., the entropy of the attribute values + for each attribute in the profiles of the nodes in the star of the given node. + If method is 'aggregate', it is computed by first aggregating each hyperedge into a single profile + (see hyperedge_aggregate_node_profile). + Else if method is 'collapse', all the node's neighbors are considered. :param h: ASH instance - :param node_id: Specify the node whose star we want to consider - :param tid: Temporal snapshot id - :param method: Select between two different methods of computing the star entropy for each node - :return: A dictionary with the entropy for each attribute in the star of node_id - """ + :param node_id: Specify the node for which we want to calculate the star profile entropy + :param tid: Specify the temporal id + :param method: Specify the method to be used in calculating the star profile entropy. Options are 'aggregate' or 'collapse'. + + :return: A dictionary with the entropy of each attribute + + Examples + -------- + Compute the star-profile entropy for a node (aggregate method) on tid=0 with the dataset above: + + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> tid = 0 + >>> node0 = next(iter(h.nodes(start=tid, end=tid))) + >>> star_profile_entropy(h, node0, tid, method='aggregate') + {'color': np.float64(0.7706290693639405)} - star = h.get_star(node_id, tid=tid) + """ + star = h.star(node_id, start=tid) if method == "aggregate": - attributes = list(h.get_node_profile(node_id, tid).get_attributes().keys()) profiles = [] for hyperedge_id in star: # build aggregated profile - p = NProfile(None) - for attr in attributes: - value_ = hyperedge_most_frequent_node_attribute_value( - h, hyperedge_id, attribute=attr, tid=tid - ) - if value_: - value = list(value_.keys())[0] - p.add_attribute(attr, value) - profiles.append(p) + aggr = hyperedge_aggregate_node_profile(h, hyperedge_id, tid) + profiles.append(aggr) elif method == "collapse": - nodes = [] - for hyperedge_id in star: - nodes += h.get_hyperedge_nodes(hyperedge_id) + nodes = h.neighbors(node_id, start=tid) profiles = [h.get_node_profile(n, tid) for n in set(nodes)] else: @@ -310,68 +225,54 @@ def star_profile_entropy( return res -def average_star_profile_entropy(h, tid, method: str = "aggregate") -> dict: - """ - Computes the average star profile entropy over all nodes in the ASH. For all attributes. - If method is 'aggregate', it is computed by first aggregating star hyperedges into a single profile. - Else if method is 'collapse', all the star nodes are considered. - - - :param h: ASH instance - :param tid: Temporal snapshot id - :param method: Specify how to compute the star entropies - :return: A dictionary mapping each node attribute to the average entropy value - """ - entropies = defaultdict(list) - for node_id in h.get_node_set(tid=tid): - ent = star_profile_entropy(h, node_id, method=method, tid=tid) - for attr_name, val in ent.items(): - entropies[attr_name].append(val) - - return {k: np.mean(v) for k, v in entropies.items()} - - def star_profile_homogeneity( h: ASH, node_id: int, tid: int, method: str = "aggregate" ) -> dict: """ - The star_profile_homogeneity function computes the homogeneity of a node with respect to its star. For each node - attribute value regarding the node, the function computes the relative frequency of that value among the star's - other nodes. - If method is 'aggregate', it is computed by first aggregating the hyperedges into a single profile. - Else if method is 'collapse', all the star nodes are considered. - + Returns the homogeneity of the star profile of a node, i.e., the relative frequency of the node's attribute value + for each attribute in the profiles of the nodes in the star of the given node. + If method is 'aggregate', it is computed by first aggregating each hyperedge into a single profile + (see hyperedge_aggregate_node_profile). + Else if method is 'collapse', all the node's neighbors are considered. :param h: ASH instance - :param node_id: Specify the node for which we want to calculate the star homogeneity - :param tid: Specify the temporal id - :param method: Specify the method to be used in calculating the star profile homogeneity + :param node_id: node id + :param tid: temporal id + :param method: Specify the method to be used in calculating the star profile homogeneity. Options are 'aggregate' or 'collapse'. + :return: A dictionary with the homogeneity of each attribute - """ - star = h.get_star(node_id, tid=tid) + Examples + -------- + Compute the star-profile homogeneity for a node (aggregate method) on tid=0 with the dataset above: + + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> tid = 0 + >>> node0 = next(iter(h.nodes(start=tid, end=tid))) + >>> star_profile_homogeneity(h, node0, tid, method='aggregate') + {'color': 0.7741935483870968} - attr_names = list(h.get_node_profile(node_id, tid).get_attributes().keys()) + """ + star = h.star(node_id, start=tid) - profiles = [] if method == "aggregate": + profiles = [] for hyperedge_id in star: # build aggregated profile - p = NProfile(None) - for attr in attr_names: - value_ = hyperedge_most_frequent_node_attribute_value( - h, hyperedge_id, attribute=attr, tid=tid - ) - if value_: - value = list(value_.keys())[0] - p.add_attribute(attr, value) - profiles.append(p) + aggr = hyperedge_aggregate_node_profile(h, hyperedge_id, tid) + profiles.append(aggr) elif method == "collapse": - nodes = [] - for hyperedge_id in star: - nodes += h.get_hyperedge_nodes(hyperedge_id) - profiles.extend([h.get_node_profile(n, tid) for n in set(nodes)]) + profiles = [ + h.get_node_profile(n, tid) for n in set(h.neighbors(node_id, start=tid)) + ] else: raise ValueError("method must either be 'aggregate' or 'collapse'") @@ -389,85 +290,42 @@ def star_profile_homogeneity( return res -def average_star_profile_homogeneity( - h: ASH, - tid: int, - method: str = "aggregate", - by_label: bool = True, - min_star_size: int = 2, -) -> object: +def average_group_degree(h: ASH, tid: int, hyperedge_size: int = None) -> object: """ - The average_star_profile_homogeneity function calculates the average homogeneity value for each node attribute. - If :by_label: is True, the average is computed for each attribute value. For instance, if the profiles have the - attribute 'party', which can take the values 'L' or 'R', two averages for 'party' will be computed: one over all - the stars whose central node has 'party' equal to 'L', and one over all the stars whose central node has 'party' - equal to 'R'. - - Otherwise, the average homogeneity is computed over all stars. + Computes the average degree of each group (nodes having the same label in the attribute) :param h: ASH instance - :param tid: Specify the temporal id - :param method: Specify how homogeneities are computed - :param by_label: Determine if the homogeneity is computed for each label or not - :param min_star_size: Set the minimum size of a star (in terms of number of hyperedges) to be considered - :return: A dictionary containing for each attribute, for each attribute value, the average homogeneity. - If :by_label: is False, returns a dictionary mapping each attribute to the average homogeneity over all stars. - """ - attributes = h.node_attributes_to_attribute_values(categorical=True) - if by_label: - homogeneities = { - attribute: { - attribute_value: [] for attribute_value in attributes[attribute] - } - for attribute in attributes - } - - else: - homogeneities = {attribute: [] for attribute in attributes} - - for node_id in h.get_node_set(tid=tid): - if len(h.get_star(node_id, tid=tid)) >= min_star_size: - homogeneity = star_profile_homogeneity(h, node_id, method=method, tid=tid) - for attr_name, hom in homogeneity.items(): - if by_label: - label = h.get_node_attribute(node_id, attr_name=attr_name, tid=tid) - homogeneities[attr_name][label].append(hom) - else: - homogeneities[attr_name].append(hom) - if by_label: - return { - attribute: {val: np.mean(res) for val, res in results.items()} - for attribute, results in homogeneities.items() - } - return {k: np.mean(v) for k, v in homogeneities.items()} + :param tid: the temporal id + :param hyperedge_size: Specify the size of the hyperedges + :return: A dictionary with attribute names as keys and a dictionary of average degrees for each attribute value -def average_group_degree(h: ASH, tid: int, hyperedge_size: int = None) -> object: - """ - The average_group_degree function calculates the average degree of each group (nodes having the same label in the - ASH). The function takes as input an ASH object, and returns a dictionary with keys corresponding to attributes ( - e.g., 'gender') and values corresponding to dictionaries with keys corresponding to attribute values (e.g., - 'male') and values corresponding to the average degree of nodes that have that attribute value. + Examples + -------- + Average degree by color at tid=0 with the dataset above: - :param h: ASH instance - :param hyperedge_size: Specify the size of the hyperedges - :param tid: Specify the temporal id - :return: A dictionary of dictionaries containing the average group degree + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> average_group_degree(h, tid=0) + {'color': {'red': 4.854166666666667, 'blue': 5.0}} """ - attributes = { - attr: val - for attr, val in h.node_attributes_to_attribute_values(tid=tid).items() - if isinstance(list(val)[0], str) - } + attributes = h.list_node_attributes(tid=tid, categorical=True) + group_degrees = { attribute: {attribute_value: [] for attribute_value in attributes[attribute]} for attribute in attributes } - for n in h.get_node_set(tid=tid): + for n in h.nodes(start=tid): for attr_name in attributes: - deg = h.get_degree(n, hyperedge_size=hyperedge_size, tid=tid) + deg = h.degree(n, hyperedge_size=hyperedge_size, start=tid) attr = h.get_node_attribute(n, attr_name=attr_name, tid=tid) group_degrees[attr_name][attr].append(deg) @@ -481,27 +339,52 @@ def average_group_degree(h: ASH, tid: int, hyperedge_size: int = None) -> object return res -def consistency(h: ASH) -> dict: +def attribute_consistency(h: ASH, node: int = None) -> dict: """ The consistency measures the extent to which a nodes' attribute value remains constant/change across time. The higher the value, the more consistent in time are the node's values for that attribute. :param h: ASH instance + :param node: Specify the node for which we want to calculate the consistency + :return: A dict containing, for each node, for each attribute, the consistency value + + Examples + -------- + Consistency for a specific node over time (avoid node=0 which is falsy in current implementation): + + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> attribute_consistency(h, node=1) + {'color': np.float64(0.1187091007693073)} + + Note: passing node=0 currently behaves as if no node was specified because 0 evaluates to False. """ res = defaultdict(dict) - attributes = h.node_attributes_to_attribute_values() - - for n in h.get_node_set(): - profile = h.get_node_profile(n) + attributes = h.list_node_attributes(categorical=True) + if node is not None: + nodes = [node] + else: + nodes = h.nodes() + for n in nodes: + all_profiles = h.get_node_profiles_by_time(n) for attr_name in attributes: - if profile.has_attribute(attr_name): - value = profile.get_attribute(attr_name) - labels = list(value.values()) - consist = 1 - __entropy(labels, base=len(attributes[attr_name])) - res[n][attr_name] = consist - else: - res[n][attr_name] = None + labels = [] + for time, profile in all_profiles.items(): + if profile.has_attribute(attr_name): + label = profile.get_attribute(attr_name) + labels.append(label) + + consist = 1 - __entropy(labels, base=len(attributes[attr_name])) + res[n][attr_name] = consist + if node is not None: + return res[node] return res diff --git a/ash_model/measures/clustering.py b/ash_model/measures/clustering.py index 55b4255..3dedceb 100644 --- a/ash_model/measures/clustering.py +++ b/ash_model/measures/clustering.py @@ -1,125 +1,179 @@ from math import comb +from typing import Optional -from ash_model.paths import * +from ash_model.paths import ASH, is_s_path def s_local_clustering_coefficient( - h: ASH, s: int, hyperedge_id: str, start: int = None, end: int = None + h: ASH, + s: int, + hyperedge_id: str, + start: Optional[int] = None, + end: Optional[int] = None, ) -> float: """ - The s_local_clustering_coefficient function computes the local clustering coefficient of a hyperedge in a - hypergraph. The start and end parameters are optional arguments that can be used to specify which interval should - be considered when computing this metric. If no interval is specified then all time points will be used. - - :param h: ASH instance - :param s: Specify the number of steps to take in the line graph - :param hyperedge_id: Specify the hyperedge for which to compute the local clustering coefficient - :param start: Specify the start of a time window - :param end: Specify the end of a time window - :return: The local clustering coefficient of the hyperedge with id `hyperedge_id` + Compute the local clustering coefficient of a hyperedge within the s-overlap line graph of a hypergraph. + + The local clustering coefficient is defined as the ratio of the number of edges + actually present among the neighbors of the given node to the maximum possible + number of edges among those neighbors. + + :param h: an ASH instance + :param s: minimum hyperedge overlap size for projection + :param hyperedge_id: identifier of the hyperedge in the line graph + :param start: optional start time (inclusive) + :param end: optional end time (inclusive) + + :return: local clustering coefficient in [0,1] + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> tid = 0 + >>> he0 = next(iter(h.hyperedges(start=tid, end=tid))) + >>> round(s_local_clustering_coefficient(h, 1, he0, start=tid, end=tid), 12) + 0.801169590643 """ - + # Build the s-overlap line graph once lg = h.s_line_graph(s, start, end) - if not lg.has_node(hyperedge_id): - return 1 - - ego = nx.ego_graph(lg, hyperedge_id) - ego.remove_node(hyperedge_id) + if hyperedge_id not in lg: + return 0.0 - if ego.number_of_nodes() == 0: - return 0 + # Neighbors in the line graph correspond to overlapping hyperedges + neighbors = list(lg.neighbors(hyperedge_id)) + k = len(neighbors) + if k < 2: + return 0.0 - triangle = 0 - components = nx.connected_components(ego) - for c in components: - res = [hyperedge_id] - res.extend(c) - if len(res) > 2 and is_s_path(h, res): - triangle += ego.number_of_edges() + # Induced subgraph on those neighbors + subgraph = lg.subgraph(neighbors) + actual_edges = subgraph.number_of_edges() + possible_edges = comb(k, 2) - denom = comb(2, ego.number_of_nodes()) - if denom == 0: - return 0 - LCC = triangle / denom - return LCC + return actual_edges / possible_edges def average_s_local_clustering_coefficient( - h: ASH, s: int, start: int = None, end: int = None + h: ASH, s: int, start: Optional[int] = None, end: Optional[int] = None ) -> float: """ - The average_s_local_clustering_coefficient function computes the average of the s-local clustering coefficient - for all hyperedges. - - :param h: ASH instance - :param s: Specify the number of nodes that are to be considered for each hyperedge - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :return: The average s-local clustering coefficient - - + Compute the average local clustering coefficient across all hyperedges + in the s-overlap line graph. + + :param h: an ASH instance + :param s: minimum hyperedge overlap size for projection + :param start: optional start time (inclusive) + :param end: optional end time (inclusive) + + :return: average local clustering coefficient in [0,1], or 0 if no nodes + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> round(average_s_local_clustering_coefficient(h, 1, start=0, end=0), 12) + 0.581891366366 """ + lg = h.s_line_graph(s, start, end) + n = lg.number_of_nodes() + if n == 0: + return 0.0 - LCCs = [] - count = 0 - for n in h.hyperedge_id_iterator(start, end): - count += 1 - LCCs.append(s_local_clustering_coefficient(h, s, n, start, end)) - - if count > 0: - return sum(LCCs) / count - - return 0 + total = 0.0 + for node in lg.nodes: + total += s_local_clustering_coefficient(h, s, node, start, end) + return total / n -def s_intersections(h: ASH, s: int, tid: int = None) -> int: +def s_intersections( + h: ASH, s: int, start: Optional[int] = None, end: Optional[int] = None +) -> int: """ - The s_intersections function counts the number of intersections of at least size s - between hyperedges. Parameter tid optionally specifies the temporal snapshot to analyze. - - :param h: ASH instance - :param s: Specify the minimum size of the intersection - :param tid: Specify the current time step - :return: The number of s-intersections in the hypergraph + Count the number of s-overlap intersections (edges) in the hypergraph's + s-overlap line graph. + + :param h: an ASH instance + :param s: minimum hyperedge overlap size + :param start: optional start time (inclusive) + :param end: optional end time (inclusive) + + :return: number of intersections of size >= s + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> s_intersections(h, 1, start=0, end=0) + 2091 """ + return h.s_line_graph(s, start, end).number_of_edges() - intersections = 0 - hedge_nodesets = [] - - for hyperedge_id in h.get_hyperedge_id_set(tid=tid): - nodes = h.get_hyperedge_nodes(hyperedge_id) - hedge_nodesets.append(set(nodes)) - for he1 in hedge_nodesets: - for he2 in hedge_nodesets: - if len(he1.intersection(he2)) >= s and he1 != he2: - intersections += 1 - - return intersections // 2 - - -def inclusiveness(h: ASH, tid: int = None) -> float: +def inclusiveness( + h: ASH, start: Optional[int] = None, end: Optional[int] = None +) -> float: """ - The inclusiveness function is a measure of the number of non-external hyperedges in an ASH. - It is defined as the ratio between the number of non-external hyperedges and - the hypergraph size. The higher this value, the more inclusive (or less exclusive) - the ASH is. - - :param h: ASH instance - :param tid: Specify the temporal snapshot id - :return: The ratio between the number of non-external hyperedges and the hypergraph size - + Computes the inclusiveness of the hypergraph over [start, end], defined as: + + (# of non-facet hyperedges) / (total # of hyperedges) + + A *facet* hyperedge is one that is *not* a subset of any other hyperedge. + Non-facet hyperedges are those that *are* contained in at least one strictly larger hyperedge. + + :param h: an ASH instance + :param start: optional start time (inclusive) + :param end: optional end time (inclusive) + + :return: a float in [0,1], or 0.0 if there are no hyperedges + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> inclusiveness(h, start=0, end=0) + 0.0 """ - - he_nodesets = [ - set(h.get_hyperedge_nodes(he)) for he in h.get_hyperedge_id_set(tid=tid) - ] - - non_facets = set() - for nset in he_nodesets: - for nset2 in he_nodesets: - if nset.issubset(nset2) and nset != nset2: - non_facets.add(he_nodesets.index(nset)) - - # 1 - (toplexes/hyperedges) - return len(non_facets) / len(he_nodesets) + node_sets = [set(he) for he in h.hyperedges(start, end, as_ids=False)] + total = len(node_sets) + if total == 0: + return 0.0 + + # Sort indices by descending set size to speed up subset checks + idxs = sorted(range(total), key=lambda i: len(node_sets[i]), reverse=True) + is_non_facet = [False] * total + + for i in range(total): + for j in idxs: + if i == j: + continue + if not is_non_facet[i] and node_sets[i].issubset(node_sets[j]): + is_non_facet[i] = True + break + + non_facet_count = sum(is_non_facet) + return non_facet_count / total diff --git a/ash_model/measures/hyper_conformity.py b/ash_model/measures/hyper_conformity.py index 60c47dc..e051fd3 100644 --- a/ash_model/measures/hyper_conformity.py +++ b/ash_model/measures/hyper_conformity.py @@ -1,5 +1,8 @@ -from ash_model.measures import * -from ash_model.paths.walks import * +from ash_model.paths.walks import all_shortest_s_walk_lengths, s_components +from ash_model.utils import hyperedge_most_frequent_node_attribute_value +from ash_model import ASH + +import networkx as nx from itertools import combinations from collections import defaultdict import tqdm @@ -15,6 +18,7 @@ def __label_frequency( :param u: node id :param labels: list of node categorical labels :param hierarchies: dict of labels hierarchies + :return: node profiles similarity score in [-1, 1] """ s = 1 @@ -53,6 +57,7 @@ def __label_frequency( def __distance(label: str, v1: str, v2: str, hierarchies: dict = None) -> float: """ Compute the distance of two labels in a plain hierarchy + :param label: label name :param v1: first label value :param v2: second label value @@ -73,6 +78,7 @@ def __normalize(u: object, scores: list, max_dist: int, alphas: list) -> list: :param u: node :param scores: datastructure containing the computed scores for u :param alphas: list of damping factor + :return: scores updated """ for alpha in alphas: @@ -96,6 +102,7 @@ def hyper_conformity( ) -> dict: """ Compute the Attribute-Profile Conformity for the considered graph + :param h: :param alphas: list of damping factors :param labels: list of node categorical labels @@ -103,11 +110,29 @@ def hyper_conformity( :param profile_size: :param hierarchies: label hierarchies :param tid: + :return: conformity value for each node in [-1, 1] - -- Example -- - >> g = nx.karate_club_graph() - >> pc = profile_conformity(g, 1, ['club']) + Examples + -------- + Build the dataset described in the docs and compute hyper-conformity for label 'color' at tid=0: + + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> res = hyper_conformity(h, alphas=[1], labels=['color'], s=1, profile_size=1, tid=0) + >>> len(res) + 1 + >>> ap = list(res[0].keys())[0] + >>> feat = list(res[0][ap].keys())[0] + >>> sorted(list(res[0][ap][feat].items()))[:3] + [('e1', 0.6287411100578744), ('e10', 0.5843765336901121), ('e100', 0.6358755716986335)] + """ full_res = [] @@ -136,7 +161,7 @@ def hyper_conformity( labels_value_frequency = defaultdict(lambda: defaultdict(int)) # hyperedge most frequent label - for he in b.hyperedge_id_iterator(): + for he in b.hyperedges(): for label in labels: v = list( hyperedge_most_frequent_node_attribute_value( @@ -169,7 +194,7 @@ def hyper_conformity( } for u in tqdm.tqdm(g1.nodes()): - sp = dict(all_shortest_s_walk_length(b, s, u)) + sp = dict(all_shortest_s_walk_lengths(b, s, u)) dist_to_nodes = defaultdict(list) for _, nodelist in sp.items(): diff --git a/ash_model/measures/hyper_segregation.py b/ash_model/measures/hyper_segregation.py new file mode 100644 index 0000000..f34ce09 --- /dev/null +++ b/ash_model/measures/hyper_segregation.py @@ -0,0 +1,220 @@ +from ash_model.paths.randwalks import * +from typing import Union, List, Optional, Dict +import numpy as np + +from ash_model.classes import ASH +from collections import defaultdict + + +def rwhs( + h: ASH, + s: int, + tid: int, + start_from: Union[int, str, List[Union[int, str]], None] = None, + num_walks: int = 100, + walk_length: int = 10, + p: float = 1.0, + q: float = 1.0, + edge: bool = False, + method: str = "meet", + threads: int = -1, +) -> Dict: + """ + Compute Random Walk Hypergraph Segregation (RWHS) scores for nodes in a hypergraph. + + :param h: ASH instance. + :param s: Minimum s-incidence threshold. For node walks: nodes must co-occur in at least s hyperedges. + For edge walks: hyperedges must share at least s nodes. + :param tid: Temporal snapshot id. + :param start_from: Node(s) or hyperedge id(s) from which to start the random walks. If + None, random walks will start from all nodes (or all hyperedges if edge=True). + :param num_walks: Number of random walks to perform. + :param walk_length: Length of each random walk. + :param p: Return parameter for the random walk. + :param q: In-out parameter for the random walk. + :param edge: If True, perform random walks on the hyperedge line graph. + :param method: Method to compute RWHS scores. Supported methods are 'meet' and 'jump'. + :param threads: Number of threads to use for parallel computation. Default is -1 (use all available threads). + :return: Dictionary with nodes as keys and their RWHS scores as values for each attribute + """ + + scores = defaultdict(lambda: defaultdict(float)) + walks = random_walks( + h, + start_from, + num_walks, + walk_length, + p, + q, + s, + edge, + start=tid, + end=tid, + threads=threads, + ) + + if method == "meet": + # Meet-wise RWHS is the ratio of nodes with the same attribute value as v that appear in + # a realization within W t,k, averaged over all realizations + for walk in walks: + start_node = walk[0] + for other in walk: + if start_node != other: + for attr, val in h.get_node_attributes(start_node, tid=tid).items(): + if h.get_node_attributes(other, tid=tid).get(attr) == val: + scores[start_node][attr] += 1.0 + for v in scores: + for attr in scores[v]: + scores[v][attr] /= num_walks * (walk_length - 1) + + elif method == "jump": + # jump-wise RWHS is defined as the ratio of pairs of nodes that have the same attribute value + # and are sequentially adjacent in a realization within W t,k + # averaged over all realizations + for walk in walks: + start_node = walk[0] + for i in range(len(walk) - 1): + node1 = walk[i] + node2 = walk[i + 1] + + for attr, val in h.get_node_attributes(node1, tid=tid).items(): + if h.get_node_attributes(node2, tid=tid).get(attr) == val: + scores[start_node][attr] += 1.0 + for v in scores: + for attr in scores[v]: + scores[v][attr] /= num_walks * (walk_length - 1) + else: + raise ValueError( + f"Unknown method {method}. Supported methods are 'meet' and 'jump'." + ) + return scores + + +# uses time-respecting random walks +def temporal_rwhs( + h: ASH, + s: int, + tid: int, + start_from: Optional[Union[int, str, List[Union[int, str]]]] = None, + end_at: Optional[Union[int, str]] = None, + num_walks: int = 100, + walk_length: int = 10, + p: float = 1.0, + q: float = 1.0, + method: str = "meet", + threads: int = -1, +) -> Dict: + """ + Compute Temporal Random Walk Hypergraph Segregation (RWHS) scores for nodes in a hypergraph. + + :param h: ASH instance. + :param s: Order of the hypergraph (minimum s-incidence threshold). + :param tid: Temporal snapshot id. + :param start_from: Hyperedge(s) or hyperedge id(s) from which to start the random walks. If + None, random walks will start from all hyperedges. + :param end_at: Hyperedge or hyperedge id to which to end the random walks. If None, random walks + will end at all hyperedges. + :param num_walks: Number of random walks to perform. + :param walk_length: Length of each random walk. + :param p: Return parameter for the random walk. + :param q: In-out parameter for the random walk. + :param method: Method to compute RWHS scores. Supported methods are 'meet' and 'jump'. + :param threads: Number of threads to use for parallel computation. Default is -1 (use all available threads). + :return: Dictionary with nodes as keys and their RWHS scores as values for each attribute + """ + + scores = defaultdict(lambda: defaultdict(float)) + walks = time_respecting_random_walks( + h, + s, + start_from, + end_at, + start=tid, + end=tid, + num_walks=num_walks, + walk_length=walk_length, + p=p, + q=q, + edge=True, + threads=threads, + ) + + if method == "meet": + # Meet-wise RWHS is the ratio of nodes with the same attribute value as v that appear in + # a realization within W t,k, averaged over all realizations + for walk_list in walks.values(): + for walk in walk_list: + if len(walk) == 0: + continue + + start_hyperedge = walk[0].src.split("_")[0] # Extract base hyperedge id + nodes_in_start_hyperedge = h.get_hyperedge_nodes(start_hyperedge) + + # Track all nodes visited in the walk + visited_nodes = set() + for temporal_edge in walk: + hedge_id = temporal_edge.dst.split("_")[ + 0 + ] # Extract base hyperedge id + visited_nodes.update(h.get_hyperedge_nodes(hedge_id)) + + # Compute scores for each node in the starting hyperedge + for start_node in nodes_in_start_hyperedge: + for other_node in visited_nodes: + if start_node != other_node: + start_attrs = h.get_node_attributes(start_node, tid=tid) + other_attrs = h.get_node_attributes(other_node, tid=tid) + for attr, val in start_attrs.items(): + if other_attrs.get(attr) == val: + scores[start_node][attr] += 1.0 + + # Normalize scores + total_walks = sum(len(walk_list) for walk_list in walks.values()) + if total_walks > 0: + for v in scores: + for attr in scores[v]: + # Normalize by total number of walks and average walk length + scores[v][attr] /= total_walks + + elif method == "jump": + # Jump-wise RWHS is defined as the ratio of pairs of nodes that have the same attribute value + # and are sequentially adjacent in a realization within W t,k + # averaged over all realizations + for walk_list in walks.values(): + for walk in walk_list: + if len(walk) < 2: + continue + + start_hyperedge = walk[0].src.split("_")[0] + nodes_in_start_hyperedge = h.get_hyperedge_nodes(start_hyperedge) + + # Iterate through consecutive hyperedge pairs in the walk + for i in range(len(walk) - 1): + hedge1_id = walk[i].dst.split("_")[0] + hedge2_id = walk[i + 1].dst.split("_")[0] + + nodes1 = h.get_hyperedge_nodes(hedge1_id) + nodes2 = h.get_hyperedge_nodes(hedge2_id) + + # Check all pairs of nodes from consecutive hyperedges + for node1 in nodes1: + for node2 in nodes2: + if node1 in nodes_in_start_hyperedge: + attrs1 = h.get_node_attributes(node1, tid=tid) + attrs2 = h.get_node_attributes(node2, tid=tid) + for attr, val in attrs1.items(): + if attrs2.get(attr) == val: + scores[node1][attr] += 1.0 + + # Normalize scores + total_walks = sum(len(walk_list) for walk_list in walks.values()) + if total_walks > 0: + for v in scores: + for attr in scores[v]: + scores[v][attr] /= total_walks + else: + raise ValueError( + f"Unknown method {method}. Supported methods are 'meet' and 'jump'." + ) + + return scores diff --git a/ash_model/measures/s_centralities.py b/ash_model/measures/s_centralities.py index 57c0ecf..8421439 100644 --- a/ash_model/measures/s_centralities.py +++ b/ash_model/measures/s_centralities.py @@ -1,9 +1,16 @@ +from typing import Optional + import networkx as nx + from ash_model import ASH def __s_linegraph( - h: ASH, s: int, start: int = None, end: int = None, edges: bool = True + h: ASH, + s: int, + start: Optional[int] = None, + end: Optional[int] = None, + edges: bool = True, ) -> nx.Graph: """ @@ -12,6 +19,7 @@ def __s_linegraph( :param start: :param end: :param edges: + :return: """ if edges: @@ -26,27 +34,41 @@ def __s_linegraph( def s_betweenness_centrality( h: ASH, s: int, - start: int = None, - end: int = None, + start: Optional[int] = None, + end: Optional[int] = None, edges: bool = True, normalized: bool = True, weight: bool = False, ) -> dict: """ - The s_betweenness_centrality function computes the s-betweenness centrality for each node in a hypergraph. The - betweenness centrality of a node is defined as the number of shortest s-paths from all vertices to all others - that pass through that node. - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :param normalized: Normalize the s-betweenness centrality values - :param weight: Determine if the weight of the edges should be considered - :return: A dictionary with the s-betweenness centrality of each node (or edge) in the hypergraph + Returns the betweenness centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the betweenness centrality for hyperedges (the nodes of the line graph). + If `edges` is False, it computes the betweenness centrality for nodes by first converting the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + :param normalized: if True, normalize the betweenness centrality values + :param weight: if True, use edge weights for the betweenness centrality calculation + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their betweenness centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_betweenness_centrality(h, 1, start=0, end=0).items()))[:3] + >>> head3 + [('e1', 0.0), ('e10', 0.021109461571662495), ('e100', 0.0035032472389105243)] """ - lg, node_to_eid = __s_linegraph(h, s, start, end, edges) if weight: @@ -63,18 +85,38 @@ def s_betweenness_centrality( def s_closeness_centrality( - h: ASH, s: int, start: int = None, end: int = None, edges: bool = True + h: ASH, + s: int, + start: Optional[int] = None, + end: Optional[int] = None, + edges: bool = True, ) -> dict: """ - The s_closeness_centrality function computes the s-closeness centrality of each node in a hypergraph. - The closeness centrality is defined as the inverse of the sum of s-distances from a given node to all other nodes. - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :return: A dictionary with the nodes/edges as keys and their s-closeness centrality as values + Returns the closeness centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the closeness centrality for hyperedges (the nodes of the line graph). + If `edges` is False, it computes the closeness centrality for nodes by first converting the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their closeness centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_closeness_centrality(h, 1, start=0, end=0).items()))[:3] + >>> head3 + [('e1', 0.4563758389261745), ('e10', 0.5483870967741935), ('e100', 0.40556660039761433)] """ lg, node_to_eid = __s_linegraph(h, s, start, end, edges) @@ -88,18 +130,38 @@ def s_closeness_centrality( def s_eccentricity( - h: ASH, s: int, start: int = None, end: int = None, edges: bool = True + h: ASH, + s: int, + start: Optional[int] = None, + end: Optional[int] = None, + edges: bool = True, ) -> dict: """ - The s_eccentricity function returns the s-eccentricity of each node in a given hypergraph. - The s-eccentricity of a node is the maximum s-distance between that node and any other node. - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :return: A dictionary with the nodes/edges as keys and their s-eccentricity as values + Returns the eccentricity of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the eccentricity for hyperedges (the nodes of the line graph). + If `edges` is False, it computes the eccentricity for nodes by first converting the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their eccentricity values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_eccentricity(h, 1, start=0, end=0).items()))[:3] + >>> head3 + [('e1', 4), ('e10', 3), ('e100', 4)] """ lg, node_to_eid = __s_linegraph(h, s, start, end, edges) @@ -113,18 +175,42 @@ def s_eccentricity( def s_harmonic_centrality( - h: ASH, s: int, start: int = None, end: int = None, edges: bool = True + h: ASH, + s: int, + start: Optional[int] = None, + end: Optional[int] = None, + edges: bool = True, ) -> dict: """ - The s_harmonic_centrality function computes the s-harmonic centrality of each node in a hypergraph. - The harmonic centrality is defined as the sum of the inverse of the s-distances between all nodes. - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :return: A dictionary with the nodes/edges as keys and their s-harmonic centrality as values + Returns the harmonic centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the harmonic centrality for hyperedges ( + the nodes of the line graph). + If `edges` is False, it computes the harmonic centrality for nodes by first converting + the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) + to their harmonic centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_harmonic_centrality(h, 1, start=0, end=0).items()))[:3] + >>> head3 + [('e1', 105.58333333333324), ('e10', 127.66666666666663), ('e100', 89.99999999999993)] + """ lg, node_to_eid = __s_linegraph(h, s, start, end, edges) @@ -140,39 +226,54 @@ def s_harmonic_centrality( def s_katz( h: ASH, s: int, - start: int = None, - end: int = None, + start: Optional[int] = None, + end: Optional[int] = None, edges: bool = True, - normalized: bool = True, alpha: float = 0.1, beta: float = 1.0, - weight: bool = False, + max_iter: int = 1000, + tol: float = 1e-06, + normalized: bool = True, ) -> dict: """ - The s_katz function computes the Katz s-centrality of all nodes in a hypergraph. - - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :param normalized: Normalize the centrality scores - :param alpha: Control the rate of convergence - :param beta: Control the influence of the number of s-paths on katz centrality - :param weight: Determine whether or not the weight of each edge is used in the calculation - :return: A dictionary with the katz centrality of each node/edge + Returns the Katz centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the Katz centrality for hyperedges ( + the nodes of the line graph). + If `edges` is False, it computes the Katz centrality for nodes by first converting + the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + :param normalized: if True, normalize the Katz centrality values + :param alpha: attenuation factor for the Katz centrality + :param beta: scaling factor for the Katz centrality + :param max_iter: maximum number of iterations for the Katz centrality calculation + :param tol: tolerance for the Katz centrality calculation + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their Katz centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_katz(h, 1, start=0, end=0).items()))[:3] + >>> [(k, float(v)) for k,v in head3] + [('e1', 0.015921892363685495), ('e10', -0.01107345978999999), ('e100', 0.03526804656510612)] """ lg, node_to_eid = __s_linegraph(h, s, start, end, edges) - if weight: - weight = "w" - else: - weight = None - - res = nx.katz_centrality_numpy( - lg, normalized=normalized, alpha=alpha, beta=beta, weight=weight + res = nx.katz_centrality( + lg, alpha=alpha, beta=beta, max_iter=max_iter, tol=tol, normalized=normalized ) if node_to_eid is None: return res @@ -184,34 +285,44 @@ def s_katz( def s_load_centrality( h: ASH, s: int, - start: int = None, - end: int = None, + start: Optional[int] = None, + end: Optional[int] = None, edges: bool = True, - normalized: bool = True, - weight: bool = False, + weight=None, ) -> dict: """ - The s_load_centrality function calculates the s-load centrality of all nodes in a hypergraph. - The load centrality is defined as the fraction of all shortest s-paths that pass through a given node. - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :param normalized: Normalize the centrality scores - :param weight: Determine whether or not the weight of each edge is used in the calculation - :return: A dictionary with the s-load centrality of each node/edge + Returns the load centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the load centrality for hyperedges ( + the nodes of the line graph). + If `edges` is False, it computes the load centrality for nodes by first converting + the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + :param weight: edge attribute to use as weight + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their load centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_load_centrality(h, 1, start=0, end=0).items()))[:3] + >>> head3 + [('e1', 0.0), ('e10', 0.017716537175626074), ('e100', 0.004101958933395599)] """ - lg, node_to_eid = __s_linegraph(h, s, start, end, edges) - if weight: - weight = "w" - else: - weight = None - - res = nx.load_centrality(lg, normalized=normalized, weight=weight) + res = nx.load_centrality(lg, weight=weight) if node_to_eid is None: return res else: @@ -222,35 +333,47 @@ def s_load_centrality( def s_eigenvector_centrality( h: ASH, s: int, - start: int = None, - end: int = None, + start: Optional[int] = None, + end: Optional[int] = None, edges: bool = True, - weight: bool = False, - max_iter: int = 50, - tol: float = 0, + max_iter: int = 100, + tol: float = 1e-06, + weight=None, ) -> dict: """ - The s_eigenvector_centrality function computes the eigenvector centrality for each node in a hypergraph. - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :param normalized: Normalize the centrality scores - :param weight: Determine whether the weight of each edge is used in the calculation - :param max_iter: Set the maximum number of iterations in power method eigenvalue solver - :param tol: Set the tolerance for convergence, - :return: A dictionary with the eigenvector s-centrality of each node + Returns the eigenvector centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the eigenvector centrality for hyperedges + (the nodes of the line graph). + If `edges` is False, it computes the eigenvector centrality for nodes by first + converting the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + :param max_iter: maximum number of iterations for the eigenvector centrality calculation + :param tol: tolerance for convergence in the eigenvector centrality calculation + :param weight: edge attribute to use as weight + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their eigenvector centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_eigenvector_centrality(h, 1, start=0, end=0).items()))[:3] + >>> [(k, float(v)) for k,v in head3] + [('e1', 0.12621433668406887), ('e10', 0.1777592407633311), ('e100', 0.010063200782658498)] """ - lg, node_to_eid = __s_linegraph(h, s, start, end, edges) - if weight: - weight = "w" - else: - weight = None - res = nx.eigenvector_centrality_numpy(lg, weight=weight, max_iter=max_iter, tol=tol) if node_to_eid is None: return res @@ -263,19 +386,35 @@ def s_information_centrality( h: ASH, s: int, start: int = None, end: int = None, edges: bool = True, weight=None ) -> dict: """ - The s_information_centrality function computes the information centrality of all nodes in a hypergraph The - s-information centrality is defined as the entropy of the distribution over all s-paths from a to b, where a and - b are nodes or hyperedges in the hypergraph. - - :param h: ASH instance - :param s: minimum intersection between hyperedges to form a path - :param start: Specify the start of the time window - :param end: Specify the end of the time window - :param edges: Determine whether to use the edges or nodes of the hypergraph - :param weight: Determine whether the weight of each edge is used in the calculation - :return: A dictionary with the nodes/edges as keys and their s-information centrality as values + Returns the information centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the information centrality for hyperedges + (the nodes of the line graph). + If `edges` is False, it computes the information centrality for nodes by first + converting the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + :param weight: if True, use edge weights for the information centrality calculation + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their information centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_information_centrality(h, 1, start=0, end=0).items()))[:3] + >>> head3 + [('e1', 0.036151507093556814), ('e10', 0.04152134988072226), ('e100', 0.024272445362294077)] """ - lg, node_to_eid = __s_linegraph(h, s, start, end, edges) if weight: @@ -295,17 +434,33 @@ def s_second_order_centrality( h: ASH, s: int, start: int = None, end: int = None, edges: bool = True ) -> dict: """ - The s_second_order_centrality function computes the s-second order centrality of all nodes in a hypergraph The - s-second order centrality for a node/edge is the standard deviation of the return times to that node(edge of a - perpetual random s-walk on the hypergraph: - - - :param h: Specify the graph that is being used - :param s: Specify the source node - :param start: Specify the start of a time interval, - :param end: Specify the end of a time interval - :param edges: Specify whether the edges of the line graph should be included in the - :return: A dictionary of the second order centrality for each node + Returns the second-order centrality of the nodes in the line graph of the hypergraph. + If `edges` is True, the function computes the second-order centrality for hyperedges + (the nodes of the line graph). + If `edges` is False, it computes the second-order centrality for nodes by first + converting the hypergraph to its dual. + + :param h: the ASH instance + :param s: minimum hyperedge overlap size for paths + :param start: start time of the interval + :param end: end time of the interval + :param edges: if True, compute for hyperedges; if False, compute for nodes + + :return: a dictionary mapping node IDs (or edge IDs if `edges` is True) to their second-order centrality values + + Examples + -------- + >>> import numpy as np, networkx as nx + >>> from ash_model.utils.networkx import from_networkx_maximal_cliques_list + >>> Gs = [nx.barabasi_albert_graph(100, 3, seed=i) for i in range(10)] + >>> rng = np.random.default_rng(42) + >>> for G in Gs: + ... for n in G.nodes(): + ... G.nodes[n]['color'] = 'red' if rng.integers(0, 2) == 0 else 'blue' + >>> h = from_networkx_maximal_cliques_list(Gs) + >>> head3 = sorted(list(s_second_order_centrality(h, 1, start=0, end=0).items()))[:3] + >>> head3 + [('e1', 373.1451853808109), ('e10', 226.34942005127067), ('e100', 687.213714885934)] """ lg, node_to_eid = __s_linegraph(h, s, start, end, edges) diff --git a/ash_model/models/__init__.py b/ash_model/models/__init__.py deleted file mode 100644 index 1d9e10d..0000000 --- a/ash_model/models/__init__.py +++ /dev/null @@ -1 +0,0 @@ -from .random import random_ASH diff --git a/ash_model/models/random.py b/ash_model/models/random.py deleted file mode 100644 index dc9f3fc..0000000 --- a/ash_model/models/random.py +++ /dev/null @@ -1,60 +0,0 @@ -import random - -from ash_model.classes import ASH - - -def random_ASH( - n_nodes: int, - n_hyperedges: int, - max_edge_size: int = 10, - n_tids: int = 3, - attr_to_vals_dict: dict = None, - seed: int = 42, -) -> ASH: - """ - - :param n_nodes: Number of total nodes in the ASH - :param n_hyperedges: Number of hyperedges to be added at each tid - :param max_edge_size: Maximum hyperedge size - :param n_tids: Number of temporal snapshots - :param attr_to_vals_dict: Attribute-to-attribute-values dict, to be added to each node profile - :param seed: Random seed - :return: random ASH instance - """ - random.seed(seed) - - if attr_to_vals_dict is None: - attr_to_vals_dict = {} - - h = ASH(hedge_removal=True) - # Generate random hyperedge sizes - hes_presence = dict() - nodes_presence = dict() - for tid in range(n_tids): - # Generate random hyperedges - hyperedges = [] - nodes = set() - hyperedge_sizes = [ - random.randint(2, max_edge_size) for _ in range(n_hyperedges) - ] - for size in hyperedge_sizes: - he_nodes = random.sample(range(n_nodes), size) - for node in he_nodes: - nodes.add(node) - hyperedges.append(he_nodes) - nodes_presence[tid] = nodes - hes_presence[tid] = hyperedges - - for tid, hes in hes_presence.items(): - h.add_hyperedges(hes, start=tid) - nad = { - n: { - attr_name: random.choice(attr_to_vals_dict[attr_name]) - for attr_name in attr_to_vals_dict - } - for n in nodes_presence[tid] - } - - h.add_nodes(nodes_presence[tid], start=tid, node_attr_dict=nad) - - return h diff --git a/ash_model/multiego/__init__.py b/ash_model/multiego/__init__.py new file mode 100644 index 0000000..0e66263 --- /dev/null +++ b/ash_model/multiego/__init__.py @@ -0,0 +1,23 @@ +""" +Multi-Ego Networks for temporal hypergraphs. + +This module provides functionality to extract and analyze Multi-Ego Networks, +which are hypergraph ego networks with multiple root nodes (egos). +This generalizes the single-node ego network (accessible via ASH.star()) to sets of root nodes. +""" + +from .core import get_multiego, get_fractured_multiego, get_core_multiego +from .similarity import ( + jaccard_similarity, + minimum_overlapping_similarity, + delta_similarity, +) + +__all__ = [ + "get_multiego", + "get_fractured_multiego", + "get_core_multiego", + "jaccard_similarity", + "minimum_overlapping_similarity", + "delta_similarity", +] diff --git a/ash_model/multiego/core.py b/ash_model/multiego/core.py new file mode 100644 index 0000000..d3d99b7 --- /dev/null +++ b/ash_model/multiego/core.py @@ -0,0 +1,174 @@ +""" +Core Multi-Ego Network extraction functions for temporal hypergraphs. +""" + +from typing import Set, List, Optional +from ..classes import ASH + + +def get_multiego( + h: ASH, + U: Set[int], + start: Optional[int] = None, + end: Optional[int] = None, +) -> List[Set[int]]: + """ + Extract the Multi-Ego Network for a set of ego nodes U within a time window. + + A Multi-Ego Network contains all hyperedges that include at least one node from the ego set U. + This generalizes the single-node ego network (ASH.star()) to multiple root nodes. + + :param h: an ASH instance + :param U: set of ego nodes (root nodes) + :param start: start time of the query window (optional). If None, considers all time periods. + :param end: end time of the query window (inclusive, optional). If None, only start time is considered (if start is provided), otherwise all time periods. + + :return: list of hyperedges (as sets of node IDs) forming the Multi-Ego Network + + Examples + -------- + >>> h = ASH() + >>> # ... add hyperedges ... + >>> U = {1, 2} # Two ego nodes + >>> multiego = get_multiego(h, U) # All time periods + >>> multiego = get_multiego(h, U, start=0) # Single snapshot + >>> multiego = get_multiego(h, U, start=0, end=5) # Time window [0,5] + >>> print(f"Multi-Ego Network contains {len(multiego)} hyperedges") + """ + if not U: + return [] + + multiego = [] + seen_edges = set() # Track unique hyperedges across time window + + # Get all hyperedges in the time window + hyperedge_ids = h.hyperedges(start=start, end=end, as_ids=True) + + # Iterate through all hyperedges in the time window + for edge_id in hyperedge_ids: + edge_nodes = frozenset(h.get_hyperedge_nodes(edge_id)) + + # Check if the hyperedge contains at least one node from U + # and hasn't been added yet (to avoid duplicates in time window) + if U.intersection(edge_nodes) and edge_nodes not in seen_edges: + multiego.append(set(edge_nodes)) + seen_edges.add(edge_nodes) + + return multiego + + +def get_fractured_multiego( + h: ASH, + U: Set[int], + start: Optional[int] = None, + end: Optional[int] = None, + alpha: float = 0.5, +) -> List[Set[int]]: + """ + Extract the Fractured Multi-Ego Network for a set of ego nodes U within a time window. + + A Fractured Multi-Ego Network contains all hyperedges where at least alpha*|U| nodes + from the ego set U are present. + + :param h: an ASH instance + :param U: set of ego nodes (root nodes) + :param start: start time of the query window (optional). If None, considers all time periods. + :param end: end time of the query window (inclusive, optional). If None, only start time is considered (if start is provided), otherwise all time periods. + :param alpha: fraction threshold (0 < alpha <= 1). A hyperedge is included if it contains at least alpha*|U| nodes from U. + + :return: list of hyperedges (as sets of node IDs) forming the Fractured Multi-Ego Network + + Examples + -------- + >>> h = ASH() + >>> # ... add hyperedges ... + >>> U = {1, 2, 3, 4} # Four ego nodes + >>> # Include hyperedges with at least 50% of U (2 nodes) + >>> multiego = get_fractured_multiego(h, U, alpha=0.5) # All time periods + >>> multiego = get_fractured_multiego(h, U, start=0, alpha=0.5) + >>> multiego = get_fractured_multiego(h, U, start=0, end=5, alpha=0.75) + """ + if not U or alpha <= 0 or alpha > 1: + return [] + + multiego = [] + seen_edges = set() # Track unique hyperedges across time window + threshold = alpha * len(U) + + # Get all hyperedges in the time window + hyperedge_ids = h.hyperedges(start=start, end=end, as_ids=True) + + # Iterate through all hyperedges in the time window + for edge_id in hyperedge_ids: + edge_nodes = frozenset(h.get_hyperedge_nodes(edge_id)) + + # Count how many nodes from U are in the hyperedge + intersection_size = len(U.intersection(edge_nodes)) + + # Check if the hyperedge contains at least alpha*|U| nodes from U + # and hasn't been added yet + if intersection_size >= threshold and edge_nodes not in seen_edges: + multiego.append(set(edge_nodes)) + seen_edges.add(edge_nodes) + + return multiego + + +def get_core_multiego( + h: ASH, + U: Set[int], + start: Optional[int] = None, + end: Optional[int] = None, + beta: float = 0.5, +) -> List[Set[int]]: + """ + Extract the Core Multi-Ego Network for a set of ego nodes U within a time window. + + A Core Multi-Ego Network contains all hyperedges where the nodes from U represent + at least beta fraction of the hyperedge size. + + :param h: an ASH instance + :param U: set of ego nodes (root nodes) + :param start: start time of the query window (optional). If None, considers all time periods. + :param end: end time of the query window (inclusive, optional). If None, only start time is considered (if start is provided), otherwise all time periods. + :param beta: fraction threshold (0 < beta <= 1). A hyperedge is included if nodes from U represent at least beta*|hyperedge| of its nodes. + + :return: list of hyperedges (as sets of node IDs) forming the Core Multi-Ego Network + + Examples + -------- + >>> h = ASH() + >>> # ... add hyperedges ... + >>> U = {1, 2, 3} # Three ego nodes + >>> # Include hyperedges where U nodes are at least 60% of the hyperedge + >>> multiego = get_core_multiego(h, U, beta=0.6) # All time periods + >>> multiego = get_core_multiego(h, U, start=0, beta=0.6) + >>> multiego = get_core_multiego(h, U, start=0, end=5, beta=0.5) + """ + if not U or beta <= 0 or beta > 1: + return [] + + multiego = [] + seen_edges = set() # Track unique hyperedges across time window + + # Get all hyperedges in the time window + hyperedge_ids = h.hyperedges(start=start, end=end, as_ids=True) + + # Iterate through all hyperedges in the time window + for edge_id in hyperedge_ids: + edge_nodes = frozenset(h.get_hyperedge_nodes(edge_id)) + + if len(edge_nodes) == 0: + continue + + # Count how many nodes from U are in the hyperedge + intersection_size = len(U.intersection(edge_nodes)) + + # Check if U nodes represent at least beta fraction of the hyperedge + # and hasn't been added yet + threshold = beta * len(edge_nodes) + if intersection_size >= threshold and edge_nodes not in seen_edges: + multiego.append(set(edge_nodes)) + seen_edges.add(edge_nodes) + + return multiego diff --git a/ash_model/multiego/similarity.py b/ash_model/multiego/similarity.py new file mode 100644 index 0000000..56908f3 --- /dev/null +++ b/ash_model/multiego/similarity.py @@ -0,0 +1,141 @@ +""" +Similarity measures for comparing Multi-Ego Networks. +""" + +from typing import List, Set + + +def jaccard_similarity(multiego1: List[Set[int]], multiego2: List[Set[int]]) -> float: + """ + Compute the Jaccard similarity between two Multi-Ego Networks. + + The Jaccard similarity is defined as the size of the intersection divided by + the size of the union of the two Multi-Ego Network hyperedge sets. + + :param multiego1: first Multi-Ego Network (list of hyperedges as sets of node IDs) + :param multiego2: second Multi-Ego Network (list of hyperedges as sets of node IDs) + + :return: Jaccard similarity score in [0, 1]. Returns 0.0 if both Multi-Ego Networks are empty. + + Examples + -------- + >>> multiego1 = [{1, 2}, {2, 3}, {1, 3}] + >>> multiego2 = [{1, 2}, {3, 4}] + >>> sim = jaccard_similarity(multiego1, multiego2) + >>> print(f"Jaccard similarity: {sim:.3f}") + """ + if not multiego1 and not multiego2: + return 0.0 + + # Convert hyperedges to frozensets for set operations + set1 = {frozenset(edge) for edge in multiego1} + set2 = {frozenset(edge) for edge in multiego2} + + intersection = len(set1.intersection(set2)) + union = len(set1.union(set2)) + + if union == 0: + return 0.0 + + return intersection / union + + +def minimum_overlapping_similarity( + multiego1: List[Set[int]], multiego2: List[Set[int]] +) -> float: + """ + Compute the minimum overlapping similarity between two Multi-Ego Networks. + + This similarity is defined as the size of the intersection divided by + the minimum size of the two Multi-Ego Network hyperedge sets. + + :param multiego1: first Multi-Ego Network (list of hyperedges as sets of node IDs) + :param multiego2: second Multi-Ego Network (list of hyperedges as sets of node IDs) + + :return: minimum overlapping similarity score in [0, 1]. Returns 0.0 if either Multi-Ego Network is empty. + + Examples + -------- + >>> multiego1 = [{1, 2}, {2, 3}, {1, 3}] + >>> multiego2 = [{1, 2}, {3, 4}] + >>> sim = minimum_overlapping_similarity(multiego1, multiego2) + >>> print(f"Min overlapping similarity: {sim:.3f}") + """ + if not multiego1 or not multiego2: + return 0.0 + + # Convert hyperedges to frozensets for set operations + set1 = {frozenset(edge) for edge in multiego1} + set2 = {frozenset(edge) for edge in multiego2} + + intersection = len(set1.intersection(set2)) + min_size = min(len(set1), len(set2)) + + if min_size == 0: + return 0.0 + + return intersection / min_size + + +def delta_similarity(multiego1: List[Set[int]], multiego2: List[Set[int]]) -> float: + """ + Compute the delta similarity between two Multi-Ego Networks. + + This is a weighted Jaccard similarity that considers the best matching + between hyperedges based on their node overlap. For each hyperedge in the + smaller Multi-Ego Network, it finds the best match in the larger one based on Jaccard + similarity at the node level. + + :param multiego1: first Multi-Ego Network (list of hyperedges as sets of node IDs) + :param multiego2: second Multi-Ego Network (list of hyperedges as sets of node IDs) + + :return: delta similarity score in [0, 1]. Returns 0.0 if either Multi-Ego Network is empty. + + Examples + -------- + >>> multiego1 = [{1, 2, 3}, {2, 3, 4}] + >>> multiego2 = [{1, 2}, {3, 4, 5}] + >>> sim = delta_similarity(multiego1, multiego2) + >>> print(f"Delta similarity: {sim:.3f}") + """ + if not multiego1 or not multiego2: + return 0.0 + + # Ensure multiego1 is the smaller one + if len(multiego1) > len(multiego2): + multiego1, multiego2 = multiego2, multiego1 + + total_similarity = 0.0 + used_edges = set() + + # For each edge in the smaller Multi-Ego Network, find the best match in the larger one + for edge1 in multiego1: + set1 = set(edge1) + best_match_sim = 0.0 + best_match_idx = -1 + + for idx, edge2 in enumerate(multiego2): + if idx in used_edges: + continue + + set2 = set(edge2) + + # Compute Jaccard similarity at the node level + intersection = len(set1.intersection(set2)) + union = len(set1.union(set2)) + + if union > 0: + node_jaccard = intersection / union + if node_jaccard > best_match_sim: + best_match_sim = node_jaccard + best_match_idx = idx + + if best_match_idx >= 0: + used_edges.add(best_match_idx) + total_similarity += best_match_sim + + # Normalize by the size of the larger Multi-Ego Network + if len(multiego2) == 0: + return 0.0 + + return total_similarity / len(multiego2) diff --git a/ash_model/paths/__init__.py b/ash_model/paths/__init__.py index 91b6bd1..7d060a6 100644 --- a/ash_model/paths/__init__.py +++ b/ash_model/paths/__init__.py @@ -1,2 +1,3 @@ from .walks import * from .time_respecting_walks import * +from .randwalks import * diff --git a/ash_model/paths/randwalks.py b/ash_model/paths/randwalks.py new file mode 100644 index 0000000..d42cd5e --- /dev/null +++ b/ash_model/paths/randwalks.py @@ -0,0 +1,335 @@ +from typing import Any, Dict, List, Optional, Tuple, Union + +import numpy as np +from scipy import sparse +import networkx as nx +import csrgraph as cg + +from ash_model import ASH +from ash_model.paths import temporal_s_dag, TemporalEdge + + +def _normalize_rows(matrix: np.ndarray) -> np.ndarray: + """ + Normalize each row of a numpy matrix so that rows sum to 1. + """ + row_sums = matrix.sum(axis=1, keepdims=True) + row_sums[row_sums == 0] = 1.0 + return matrix / row_sums + + +def _map_to_indices(items: List[Any]) -> Tuple[Dict[Any, int], Dict[int, Any]]: + """ + Create forward and reverse mappings between items and integer indices. + """ + fwd = {item: idx for idx, item in enumerate(items)} + rev = {idx: item for item, idx in fwd.items()} + return fwd, rev + + +def _build_node_transition_matrix( + h: ASH, s: int, start: Optional[int], end: Optional[int] +) -> Tuple[sparse.csr_matrix, Dict[Any, int]]: + """ + Construct transition probability matrix between nodes in hyperedges. + + :param h: ASH hypergraph object + :param s: Minimum s-incidence threshold (nodes must co-occur in at least s hyperedges) + :param start: Lower temporal bound + :param end: Upper temporal bound + """ + nodes = list(h.nodes(start=start, end=end)) + n2idx, _ = _map_to_indices(nodes) + n = len(nodes) + + # Track co-occurrence counts between node pairs + cooccurrence_counts: Dict[Tuple[Any, Any], int] = {} + + for edge in h.hyperedges(start=start, end=end, as_ids=False): + vertices = list(edge) + for u in vertices: + for v in vertices: + if u != v: + pair = (u, v) + cooccurrence_counts[pair] = cooccurrence_counts.get(pair, 0) + 1 + + # Build transition matrix only for pairs with >= s co-occurrences + T = np.zeros((n, n), dtype=float) + for (u, v), count in cooccurrence_counts.items(): + if count >= s: + # Weight by number of co-occurrences + T[n2idx[u], n2idx[v]] += count + + T = _normalize_rows(T) + return sparse.csr_matrix(T), n2idx + + +def _build_edge_transition_matrix( + h: ASH, s: int, start: Optional[int], end: Optional[int] +) -> Tuple[sparse.csr_matrix, Dict[Any, int]]: + """ + Construct transition probability matrix on the line graph of hyperedges. + + :param h: ASH hypergraph object + :param s: Minimum size of node intersection between hyperedges + :param start: Lower temporal bound + :param end: Upper temporal bound + """ + G = h.s_line_graph(s=s, start=start, end=end) + nodes = sorted(G.nodes()) + n2idx, _ = _map_to_indices(nodes) + + A = nx.to_numpy_array(G, nodelist=nodes, dtype=float) + A = _normalize_rows(A) + return sparse.csr_matrix(A), n2idx + + +def random_walk_probabilities( + h: ASH, + s: int = 1, + start: Optional[int] = None, + end: Optional[int] = None, + edge: bool = False, +) -> Tuple[sparse.csr_matrix, Dict[Any, int]]: + """ + Compute CSR transition matrix and index mapping for nodes or hyperedges. + + :param h: ASH hypergraph object + :param s: Minimum s-incidence threshold (for nodes: co-occurrence count; for edges: intersection size) + :param start: Lower temporal bound + :param end: Upper temporal bound + :param edge: If True, compute for hyperedge line graph + """ + if edge: + return _build_edge_transition_matrix(h, s, start, end) + return _build_node_transition_matrix(h, s, start, end) + + +def random_walks( + h: ASH, + start_from: Union[int, str, List[Union[int, str]], None] = None, + num_walks: int = 100, + walk_length: int = 10, + p: float = 1.0, + q: float = 1.0, + s: int = 1, + edge: bool = False, + start: Optional[int] = None, + end: Optional[int] = None, + threads: int = -1, +) -> np.ndarray: + """ + Generate biased random walks on ASH hypergraph (node or edge graph). + + :param h: ASH hypergraph object + :param start_from: Node or list of nodes to start walks from + :param num_walks: Number of walks per start node + :param walk_length: Length of each walk + :param p: Return parameter (higher values make walk less likely to return to previous node) + :param q: In-out parameter (higher values make walk more local, lower values encourage exploration) + :param s: Minimum s-incidence threshold. For node walks: nodes must co-occur in at least s hyperedges to be connected. For edge walks: hyperedges must share at least s nodes to be connected. + :param edge: If True, walk on hyperedge line graph + :param start: Lower temporal bound + :param end: Upper temporal bound + :param threads: Parallel threads for random walk computation + + :returns: Array of walks (each walk is a list of original node/edge IDs) + + Examples + -------- + .. code-block:: python + + # Node-based random walks with s=1 (any co-occurrence) + walks = random_walks(h, num_walks=100, walk_length=10, s=1) + + # Node-based random walks with s=2 (nodes must co-occur in at least 2 hyperedges) + walks = random_walks(h, num_walks=100, walk_length=10, s=2) + + # Hyperedge-based random walks with s=2 (hyperedges must share at least 2 nodes) + walks = random_walks(h, num_walks=100, walk_length=10, s=2, edge=True) + """ + T_csr, n2idx = random_walk_probabilities(h, s, start, end, edge=edge) + idx2n = {idx: node for node, idx in n2idx.items()} + G = cg.csrgraph(T_csr, threads=threads) + + if start_from is None: + start_nodes = None + else: + if not isinstance(start_from, list): + start_from = [start_from] + start_nodes = [n2idx[item] for item in start_from] + + raw = G.random_walks( + walklen=walk_length, + epochs=num_walks, + start_nodes=start_nodes, + return_weight=1.0 / p, + neighbor_weight=1.0 / q, + ) + + return np.array([[idx2n[idx] for idx in walk] for walk in raw]) + + +def time_respecting_random_walks( + h: ASH, + s: int, + start_from: Optional[Union[int, str, List[Union[int, str]]]] = None, + stop_at: Optional[Union[int, str]] = None, + start: Optional[int] = None, + end: Optional[int] = None, + num_walks: int = 100, + walk_length: int = 10, + p: float = 1.0, + q: float = 1.0, + edge: bool = False, + threads: int = -1, +) -> Union[np.ndarray, Dict[Tuple[str, str], List[List[TemporalEdge]]]]: + """ + Generate biased, time-respecting random walks on the temporal hypergraph. + + This function builds a time-respecting transition matrix and uses it to guide + random walks that respect temporal ordering. The approach uses the temporal DAG + structure where all edges are forward-in-time transitions (t -> t' where t' > t). + + Semantics: + - All transitions are forward-in-time, respecting strict temporal ordering + - Each step moves to a strictly later timestamp + - Walks terminate when no forward neighbors exist (reached a temporal sink) + + :param h: ASH hypergraph object + :param s: Minimum s-incidence threshold + :param start_from: Node or edge (or list) to start walks from + :param stop_at: Node or edge to stop walks at (optional) + :param start: Lower temporal bound + :param end: Upper temporal bound + :param num_walks: Number of walks per start node/edge + :param walk_length: Length of each walk (number of transitions) + :param p: Return parameter (higher values discourage returning to previous node) + :param q: In-out parameter (higher values favor local exploration) + :param edge: If True, walk on hyperedge line graph and return TemporalEdge dict + :param threads: Parallel threads for random walk computation (currently unused in custom logic) + + :returns: If edge=False, ndarray of node ID sequences. If edge=True, dict mapping (start, end) to lists of TemporalEdge walks. + + Examples + -------- + .. code-block:: python + + # Time-respecting node walks + walks = time_respecting_random_walks(h, s=1, num_walks=100, walk_length=10) + + # Time-respecting hyperedge walks + walks_dict = time_respecting_random_walks(h, s=2, num_walks=100, walk_length=10, edge=True) + + # Start from specific nodes + walks = time_respecting_random_walks(h, s=1, start_from=[1, 2], num_walks=50) + """ + # Build temporal DAG + DAG, sources, _ = temporal_s_dag( + h, s, start_from, stop_at, start=start, end=end, edge=edge + ) + + # Build neighbor maps: all edges are now forward-in-time (time-respecting) + # There are NO same-timestamp transitions in the corrected implementation + nodes = [n for n in DAG.nodes() if isinstance(n, str) and "_" in n] + neighbors: Dict[str, List[Tuple[str, float]]] = {} + + for u, v, attrs in DAG.edges(data=True): + if "_" not in str(u) or "_" not in str(v): + continue + # All edges are forward-in-time transitions (t -> t' where t' > t) + neighbors.setdefault(str(u), []).append( + (str(v), float(attrs.get("weight", 1.0))) + ) + + # Helper to choose a neighbor by weights + def pick_weighted(neis: List[Tuple[str, float]]) -> Optional[str]: + if not neis: + return None + vs, ws = zip(*neis) + ws = np.array(ws, dtype=float) + s_sum = ws.sum() + if s_sum <= 0: + ws = np.ones_like(ws) / len(ws) + else: + ws = ws / s_sum + idx = np.random.choice(len(vs), p=ws) + return vs[idx] + + # Determine start nodes + if start_from is None: + start_nodes = [n for n in sources if n in neighbors or n in nodes] + else: + if not isinstance(start_from, list): + start_from = [start_from] + bases = set(str(sf) for sf in start_from) + start_nodes = [n for n in nodes if n.split("_")[0] in bases] + + if edge: + from collections import defaultdict + + res: Dict[Tuple[str, str], List[List[TemporalEdge]]] = defaultdict(list) + + for s_node in start_nodes: + for _ in range(num_walks): + path: List[TemporalEdge] = [] + cur = s_node + steps = 0 + + while steps < walk_length: + neis = neighbors.get(cur, []) + if not neis: + # No outgoing edges - walk reached a temporal sink + break + + nxt = pick_weighted(neis) + if nxt is None: + break + + # Append step (time-respecting: cur_t -> nxt_t' where t' > t) + fr, ft = cur.split("_") + to, tt = nxt.split("_") + w = next((w for v, w in neis if v == nxt), 1.0) + path.append(TemporalEdge(fr, to, float(w), int(tt))) + steps += 1 + cur = nxt + + if stop_at and (to == str(stop_at) or nxt == str(stop_at)): + break + + if path: + key = (path[0].fr, path[-1].to) + res[key].append(path) + + return dict(res) + else: + walks: List[List[Union[int, str]]] = [] + + for s_node in start_nodes: + for _ in range(num_walks): + seq: List[Union[int, str]] = [] + cur = s_node + steps = 0 + + while steps < walk_length: + neis = neighbors.get(cur, []) + if not neis: + # No outgoing edges - walk reached a temporal sink + break + + nxt = pick_weighted(neis) + if nxt is None: + break + + base = nxt.split("_")[0] + seq.append(base) + steps += 1 + cur = nxt + + if stop_at is not None and str(base) == str(stop_at): + break + + if seq: + walks.append(seq) + + return np.array(walks, dtype=object) diff --git a/ash_model/paths/time_respecting_walks.py b/ash_model/paths/time_respecting_walks.py index b5056fe..0a72a79 100644 --- a/ash_model/paths/time_respecting_walks.py +++ b/ash_model/paths/time_respecting_walks.py @@ -1,39 +1,54 @@ import copy +from collections import defaultdict +from dataclasses import dataclass +from typing import Tuple, Optional, List, Union + import networkx as nx import numpy as np -from collections import defaultdict, namedtuple + from ash_model import ASH -TemporalEdge = namedtuple("TemporalEdge", "fr to weight tid") -TemporalEdge.__new__.__defaults__ = (None,) * len(TemporalEdge._fields) + +# A temporal edge in an s-walk: from-hyperedge id, to-hyperedge id, weight, and timestamp. +@dataclass(frozen=True) +class TemporalEdge: + fr: str + to: str + weight: float + tid: int def temporal_s_dag( h: ASH, s: int, - hyperedge_from: str, - hyperedge_to: str = None, - start: int = None, - end: int = None, -) -> nx.DiGraph: + start_from: Optional[Union[int, str, List[Union[int, str]]]] = None, + stop_at: Optional[Union[int, str]] = None, + start: Optional[int] = None, + end: Optional[int] = None, + edge: bool = False, +) -> Tuple[nx.DiGraph, List[str], List[str]]: """ - - :param h: - :param s: - :param hyperedge_from: - :param hyperedge_to: - :param start: - :param end: - :return: + Build a time-respecting DAG over [start, end] for either hyperedges (edge=True) or nodes (edge=False). + Nodes are labeled as "_". + Edges connect items from different timestamps following chronological order, ensuring time-respecting properties. + Only forward-in-time edges are created: from timestamp t to timestamps t' where t' > t. + + :param h: The source hypergraph. + :param s: Minimum s-incidence threshold. + :param start_from: Node or hyperedge id(s) to start from. If None, starts from all items present at the first snapshot in range. + :param stop_at: Node or hyperedge id to stop at (optional). + :param start: First snapshot ID to include. Defaults to earliest. + :param end: Last snapshot ID to include. Defaults to latest. + :param edge: If True, operate on hyperedges. If False, operate on nodes. + :returns: (DAG, sources, targets) with labels "_". + :raises ValueError: If the [start, end] interval is not a valid subset of the hypergraph's snapshot IDs. """ ids = h.temporal_snapshots_ids() if len(ids) == 0: return nx.DiGraph(), [], [] - # correcting missing values if end is None: end = ids[-1] - if start is None: start = ids[0] @@ -43,325 +58,318 @@ def temporal_s_dag( f"{[min(ids), max(ids)]}." ) - # adjusting temporal window - start = list([i >= start for i in ids]).index(True) - end = end if end == ids[-1] else list([i >= end for i in ids]).index(True) - ids = ids[start : end + 1] + start_idx = next(i for i, t in enumerate(ids) if t >= start) + end_idx = max(i for i, t in enumerate(ids) if t <= end) + ids = ids[start_idx : end_idx + 1] + + # Normalize seeds to list[str] + if start_from is None: + seeds: List[str] = [] + elif isinstance(start_from, (list, tuple, set)): + seeds = [str(x) for x in start_from] + else: + seeds = [str(start_from)] - # creating empty DAG DG = nx.DiGraph() - DG.add_node(hyperedge_from) - active = {hyperedge_from: None} sources, targets = {}, {} - for tid in ids: - to_remove = [] - to_add = [] - - for an in active: - if not h.has_hyperedge_id(str(an).split("_")[0], tid=tid): - continue + # First pass: build all edges and collect reachable items + all_edges = [] + item_at_time = defaultdict(set) # Track which items exist at which times - neighbors = { - f"{n[0]}_{tid}": n[1] - for n in h.get_s_incident( - str(an).split("_")[0], s=s, start=tid, end=tid - ) - } - - if hyperedge_to is not None: - if f"{hyperedge_to}_{tid}" in neighbors: - targets[f"{hyperedge_to}_{tid}"] = None + for i, tid in enumerate(ids): + # Track items present at this timestamp + if edge: + for he in h.hyperedges(start=tid, end=tid): + item_at_time[tid].add(str(he)) + else: + for n in h.nodes(start=tid, end=tid): + item_at_time[tid].add(str(n)) + + # Build connections to all future timestamps + for future_idx in range(i + 1, len(ids)): + future_tid = ids[future_idx] + + if edge: + # For edge mode: find s-incident hyperedges at future timestamp + for he in h.hyperedges(start=tid, end=tid): + he_id = str(he) + raw_neighbors = h.get_s_incident( + he_id, s=s, start=future_tid, end=future_tid + ) + for n_id, w in raw_neighbors: + if n_id != he_id: + all_edges.append( + (f"{he_id}_{tid}", f"{n_id}_{future_tid}", w) + ) else: - for k in neighbors: - targets[k] = None - - if len(neighbors) == 0 and an != hyperedge_from: - to_remove.append(an) - - for n in neighbors: - if "_" not in an: - an = f"{an}_{tid}" - sources[an] = None - - DG.add_edge(an, n, weight=neighbors[n]) - to_add.append(n) - - for n in to_add: - active[n] = None - - for rm in to_remove: - del active[rm] - - targets = [t for t in targets if t.split("_")[0] != hyperedge_from] - - return DG, list(sources), list(targets) + # For node mode: find co-members at future timestamp + node_neighbors_future: dict[str, dict[str, int]] = defaultdict( + lambda: defaultdict(int) + ) + for he in h.hyperedges(start=future_tid, end=future_tid): + he_nodes = list(h.get_hyperedge_nodes(he)) + for ii in range(len(he_nodes)): + u = str(he_nodes[ii]) + for j in range(len(he_nodes)): + if ii == j: + continue + v = str(he_nodes[j]) + node_neighbors_future[u][v] += 1 + + # Process nodes active at current tid + for n in h.nodes(start=tid, end=tid): + n_id = str(n) + counts = node_neighbors_future.get(n_id, {}) + for v, c in counts.items(): + if c >= s and v != n_id: + all_edges.append((f"{n_id}_{tid}", f"{v}_{future_tid}", c)) + + # Add all edges to graph + for u, v, w in all_edges: + DG.add_edge(u, v, weight=w) + + # Determine sources based on start_from + if seeds: + # If seeds specified, sources are only at timestamps where seed items have outgoing edges + for seed_id in seeds: + for tid in ids: + node_label = f"{seed_id}_{tid}" + # Check if this seed exists at this time and has outgoing edges + if ( + seed_id in item_at_time[tid] + and DG.has_node(node_label) + and DG.out_degree[node_label] > 0 + ): + sources[node_label] = None + else: + # If no seeds, sources are all items at the first timestamp with outgoing edges + first_tid = ids[0] + for item_id in item_at_time[first_tid]: + node_label = f"{item_id}_{first_tid}" + if DG.has_node(node_label) and DG.out_degree[node_label] > 0: + sources[node_label] = None + + # Determine targets + if stop_at is not None: + # Only nodes matching stop_at are targets + stop_id = str(stop_at) + for tid in ids: + node_label = f"{stop_id}_{tid}" + if DG.has_node(node_label) and DG.in_degree[node_label] > 0: + targets[node_label] = None + else: + # All reachable nodes (except sources) are potential targets + for node in DG.nodes(): + if node not in sources and DG.in_degree[node] > 0: + targets[node] = None + + excluded_ids = set(str(s).split("_")[0] for s in seeds) if seeds else set() + final_targets = [t for t in targets if t.split("_")[0] not in excluded_ids] + return DG, list(sources), final_targets def time_respecting_s_walks( h: ASH, s: int, - hyperedge_from: str, - hyperedge_to: str = None, + start_from: Union[str, List[str]], + stop_at: Optional[str] = None, start: int = None, end: int = None, sample: float = 1, ) -> dict: """ - The time_respecting_s_walks function takes as input a ASH, a positive integer s, and two hyperedges. - It returns the temporal s-paths that are time-respecting with respect to the given hyperedges. - The returned value is a dictionary whose keys are pairs of nodes (from_node, to_node) and values are lists of temporal paths. - - :param h: ASH instance - :param s: minimum intersection between two hyperedges to be included in the path - :param hyperedge_from:str: Specify the source hyperedge - :param hyperedge_to:str=None: Specify the hyperedge to which we want to find all time-respecting paths - :param start:int=None: Specify the start time of the temporal network - :param end:int=None: Specify the end time of the hyperedge - :param sample:float=1: - :param : - :return: A dictionary of the form {(hyperedge_from, hyperedge_to): [list of paths]} - :doc-author: Trelent - """ - """ + Enumerate all time-respecting s-walks between a given source and optionally a target hyperedge. - :param h: - :param s: - :param hyperedge_from: - :param hyperedge_to: - :param start: - :param end: - :param sample: - :return: - """ + :param h: The source hypergraph. + :param s: Minimum number of shared nodes for s-incidence. + :param start_from: ID o lista di iperarchi da cui partire. + :param stop_at: Se fornito, considera solo cammini che terminano a questo iperarco. + :param start: First snapshot to include. + :param end: Last snapshot to include. + :param sample: Fraction of source-target pairs to sample (0 < sample <= 1). + :returns: Mapping (start_edge, end_edge) -> list of walks (TemporalEdge lists). + """ DAG, sources, targets = temporal_s_dag( - h, s, hyperedge_from, hyperedge_to, start=start, end=end + h, s, start_from=start_from, stop_at=stop_at, start=start, end=end, edge=True ) pairs = [(x, y) for x in sources for y in targets] - if sample < 1: to_sample = int(len(pairs) * sample) - pairs_idx = np.random.choice(len(pairs), size=to_sample, replace=False) - pairs = np.array(pairs)[pairs_idx] + idxs = np.random.choice(len(pairs), size=to_sample, replace=False) + pairs = [pairs[i] for i in idxs] paths = [] - for pair in pairs: - path = list(nx.all_simple_paths(DAG, pair[0], pair[1])) - - for p in path: - pt = [] - for first, second in zip(p, p[1:]): - hyperedge_from = first.split("_") - if len(hyperedge_from) == 2: - hyperedge_from = hyperedge_from[0] - else: - hyperedge_from = "_".join(hyperedge_from[0:-1]) - - hyperedge_to = second.split("_") - if len(hyperedge_to) == 2: - t = hyperedge_to[1] - hyperedge_to = hyperedge_to[0] - else: - t = hyperedge_to[-1] - hyperedge_to = "_".join(hyperedge_to[0:-1]) - - pt.append( - TemporalEdge( - hyperedge_from, - hyperedge_to, - DAG[first][second]["weight"], - int(t), - ) - ) - # check ping pong - - flag = True - if len(pt) > 1: - s = pt[0] - for l in pt[1:]: - if l[0] == s[1] and l[1] == s[0] or l[2] == s[2]: - flag = False - continue - s = l - - if flag: - paths.append(pt) - - pa = list(dict.fromkeys([tuple(x) for x in paths])) - + for src, dst in pairs: + for path_nodes in nx.all_simple_paths(DAG, src, dst): + seq = [] + for u, v in zip(path_nodes, path_nodes[1:]): + t_from = int(u.split("_")[-1]) + t_to = int(v.split("_")[-1]) + w = DAG[u][v]["weight"] + seq.append(TemporalEdge(u.split("_")[0], v.split("_")[0], w, t_to)) + + # Validate time-respecting property: each step must happen at a strictly later time + if len(seq) > 0: + valid = True + prev_edge = seq[0] + for edge in seq[1:]: + # Each edge must occur at a strictly later timestamp + if edge.tid <= prev_edge.tid: + valid = False + break + # Also reject immediate back-and-forth between same pair of nodes + if edge.fr == prev_edge.to and edge.to == prev_edge.fr: + valid = False + break + prev_edge = edge + + if valid: + paths.append(seq) + + unique = list({tuple(w): w for w in paths}.values()) res = defaultdict(list) - for p in pa: - k = (p[0][0], p[-1][1]) - res[k].append(p) + for w in unique: + key = (w[0].fr, w[-1].to) + res[key].append(w) return res def all_time_respecting_s_walks( - h: ASH, s: int, start: int = None, end: int = None, sample: float = 1 + h: ASH, + s: int, + start: int = None, + end: int = None, + sample: float = 1, ) -> dict: """ + Compute time-respecting s-walks originating from every hyperedge in the graph. + + :param h: The hypergraph. + :param s: Minimum s-incidence threshold. + :param start: Earliest snapshot to include. + :param end: Latest snapshot to include. + :param sample: Fraction of source-target samples per origin. - :param h: - :param s: - :param start: - :param end: - :param sample: - :return: + :returns: Mapping (origin_edge, destination_edge) -> list of walks. """ res = {} - for he in h.hyperedge_id_iterator(): - paths = time_respecting_s_walks( + for he in h.hyperedges(start=start, end=end): + subpaths = time_respecting_s_walks( h, - s=s, - hyperedge_from=he, - hyperedge_to=None, + s, + start_from=he, + stop_at=None, start=start, end=end, sample=sample, ) - if len(paths) > 0: - for k, path in paths.items(): - v = k[-1] - res[(he, v)] = path - + for key, walks in subpaths.items(): + if walks: + res[(he, key[1])] = walks return res def annotate_walks(paths: list) -> dict: """ + Annotate a list of s-walks with standard path metrics. - :param h: - :param paths: - :return: - """ - annotated = { - "shortest": [], - "fastest": [], - "shortest_fastest": [], - "shortest_heaviest": [], - "fastest_shortest": [], - "fastest_heaviest": [], - "foremost": [], - "heaviest": [], - "heaviest_fastest": [], - "heaviest_shortest": [], - } - - min_to_reach = None - shortest = None - fastest = None - p_weight = None - - for path in paths: - length = walk_length(path) - duration = walk_duration(path) - weight = walk_weight(path) - reach = path[-1][-1] - - if p_weight is None or weight > p_weight: - p_weight = weight - annotated["heaviest"] = [copy.copy(path)] - else: - annotated["heaviest"].append(copy.copy(path)) - - if shortest is None or length < shortest: - shortest = length - annotated["shortest"] = [copy.copy(path)] - elif length == shortest: - annotated["shortest"].append(copy.copy(path)) - - if fastest is None or duration < fastest: - fastest = duration - annotated["fastest"] = [copy.copy(path)] - elif duration == fastest: - annotated["fastest"].append(copy.copy(path)) - - if min_to_reach is None or reach < min_to_reach: - min_to_reach = reach - annotated["foremost"] = [copy.copy(path)] - elif reach == min_to_reach: - annotated["foremost"].append(copy.copy(path)) - - fastest_shortest = { - tuple(path): walk_duration(path) for path in annotated["shortest"] - } - minval = min(fastest_shortest.values()) - fastest_shortest = list( - [x for x in fastest_shortest if fastest_shortest[x] == minval] - ) - - fastest_heaviest = { - tuple(path): walk_duration(path) for path in annotated["heaviest"] - } - minval = min(fastest_heaviest.values()) - fastest_heaviest = list( - [x for x in fastest_heaviest if fastest_heaviest[x] == minval] - ) - - shortest_fastest = {tuple(path): walk_length(path) for path in annotated["fastest"]} - minval = min(shortest_fastest.values()) - shortest_fastest = list( - [x for x in shortest_fastest if shortest_fastest[x] == minval] - ) + :param paths: The walks to classify. - shortest_heaviest = { - tuple(path): walk_weight(path) for path in annotated["heaviest"] + :returns: Dictionary of metric names to lists of walks. + """ + metrics = [] + for p in paths: + length = len(p) + duration = p[-1].tid - p[0].tid + weight = sum(e.weight for e in p) + reach = p[-1].tid + metrics.append( + { + "path": p, + "length": length, + "duration": duration, + "weight": weight, + "reach": reach, + } + ) + shortest = min(metrics, key=lambda m: m["length"])["length"] + fastest = min(metrics, key=lambda m: m["duration"])["duration"] + heaviest = max(metrics, key=lambda m: m["weight"])["weight"] + foremost = min(metrics, key=lambda m: m["reach"])["reach"] + + def by(key, op, val): + return [m["path"] for m in metrics if op(m[key], val)] + + return { + "shortest": by("length", lambda x, y: x == y, shortest), + "fastest": by("duration", lambda x, y: x == y, fastest), + "heaviest": by("weight", lambda x, y: x == y, heaviest), + "foremost": by("reach", lambda x, y: x == y, foremost), + "shortest_fastest": by( + "duration", + lambda x, y: x == y, + min(m["duration"] for m in metrics if m["length"] == shortest), + ), + "shortest_heaviest": by( + "weight", + lambda x, y: x == y, + max(m["weight"] for m in metrics if m["length"] == shortest), + ), + "fastest_shortest": by( + "length", + lambda x, y: x == y, + min(m["length"] for m in metrics if m["duration"] == fastest), + ), + "fastest_heaviest": by( + "weight", + lambda x, y: x == y, + max(m["weight"] for m in metrics if m["duration"] == fastest), + ), + "heaviest_fastest": by( + "duration", + lambda x, y: x == y, + max(m["duration"] for m in metrics if m["weight"] == heaviest), + ), + "heaviest_shortest": by( + "length", + lambda x, y: x == y, + max(m["length"] for m in metrics if m["weight"] == heaviest), + ), } - minval = min(shortest_heaviest.values()) - shortest_heaviest = list( - [x for x in shortest_heaviest if shortest_heaviest[x] == minval] - ) - - heaviest_shortest = { - tuple(path): walk_weight(path) for path in annotated["shortest"] - } - maxval = max(heaviest_shortest.values()) - heaviest_shortest = list( - [x for x in heaviest_shortest if heaviest_shortest[x] == maxval] - ) - - heaviest_fastest = {tuple(path): walk_weight(path) for path in annotated["fastest"]} - maxval = max(heaviest_fastest.values()) - heaviest_fastest = list( - [x for x in heaviest_fastest if heaviest_fastest[x] == maxval] - ) - - annotated["fastest_shortest"] = [list(p) for p in fastest_shortest] - annotated["fastest_heaviest"] = [list(p) for p in fastest_heaviest] - annotated["shortest_fastest"] = [list(p) for p in shortest_fastest] - annotated["shortest_heaviest"] = [list(p) for p in shortest_heaviest] - annotated["heaviest_shortest"] = [list(p) for p in heaviest_shortest] - annotated["heaviest_fastest"] = [list(p) for p in heaviest_fastest] - - return annotated def walk_length(path: list) -> int: """ + Compute the number of edges in a temporal walk. - :param path: - :return: + :param path: The walk to measure. + + :returns: Number of steps in the walk. """ return len(path) def walk_duration(path: list) -> int: """ + Compute the duration of a temporal walk. - :param path: - :return: - """ + :param path: The walk to measure. - return int(path[-1][-1]) - int(path[0][-1]) + :returns: Time difference between first and last edge. + """ + return int(path[-1].tid) - int(path[0].tid) def walk_weight(path: list) -> int: """ + Compute the total weight of a temporal walk. + + :param path: The walk to measure. - :param path: - :return: + :returns: Cumulative weight of the walk. """ - return sum([p.weight for p in path]) + return sum(p.weight for p in path) diff --git a/ash_model/paths/walks.py b/ash_model/paths/walks.py index 45e7aee..814f65c 100644 --- a/ash_model/paths/walks.py +++ b/ash_model/paths/walks.py @@ -1,6 +1,8 @@ -import networkx as nx from collections import defaultdict, Counter from itertools import combinations +from typing import Iterator, List, Dict, Optional, Union, Tuple + +import networkx as nx from ash_model import ASH @@ -8,246 +10,327 @@ def all_simple_paths( h: ASH, s: int, - hyperedge_a: str = None, - hyperedge_b: str = None, - start: int = None, - end: int = None, - cutoff: int = None, -) -> object: + hyperedge_a: Optional[str] = None, + hyperedge_b: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, + cutoff: Optional[int] = None, +) -> Iterator[List[str]]: """ + Generate all simple, s-overlap-valid paths in a hypergraph's line graph. - :param h: - :param s: - :param hyperedge_a: - :param hyperedge_b: - :param start: - :param end: - :param cutoff: - :return: - """ + A simple path is one with no repeated hyperedges, and additionally, the + sequence must satisfy the s-overlap condition in the original hypergraph. - g = h.s_line_graph(s, start, end) + Internally, this projects the hypergraph into its s-line-graph and then + yields each NetworkX simple path that also passes the is_s_path filter. - if hyperedge_a is not None and hyperedge_b is not None: - if not g.has_node(hyperedge_a) or not g.has_node(hyperedge_b): - return [] - elif hyperedge_a is not None and not g.has_node(hyperedge_a): - return [] + :param h: ASH hypergraph instance. + :param s: Minimum overlap size between consecutive hyperedges. + :param hyperedge_a: Identifier of the starting hyperedge (optional). If None, + paths may start from any node. + :param hyperedge_b: Identifier of the ending hyperedge (optional). If None, + paths may end at any node. + :param start: Lower time bound for hyperedges (inclusive). + :param end: Upper time bound for hyperedges (inclusive). + :param cutoff: Maximum path length (number of nodes) to explore. - for p in nx.all_simple_paths(g, hyperedge_a, hyperedge_b, cutoff): - if is_s_path(h, p): - yield p + :return: Iterator over valid paths, each as a list of hyperedge IDs. + """ + # Build the s-overlap line graph + lg = h.s_line_graph(s, start, end) + + # If specific endpoints are requested, ensure they exist + if hyperedge_a and hyperedge_a not in lg: + return iter([]) + if hyperedge_b and hyperedge_b not in lg: + return iter([]) + + # Yield only the simple paths that satisfy the s-path condition + for path in nx.all_simple_paths( + lg, source=hyperedge_a, target=hyperedge_b, cutoff=cutoff + ): + if is_s_path(h, path): + yield path def shortest_s_path( h: ASH, s: int, - hyperedge_a: str = None, - hyperedge_b: str = None, - start: int = None, - end: int = None, -) -> object: - """ - - :param h: - :param s: - :param hyperedge_a: - :param hyperedge_b: - :param start: - :param end: - :return: + hyperedge_a: str, + hyperedge_b: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, + cutoff: Optional[int] = None, +) -> List[List[str]]: """ + Return all shortest simple, s-overlap-valid paths between two hyperedges. - paths = list(all_simple_paths(h, s, hyperedge_a, hyperedge_b, start, end)) - min_len = min([len(p) for p in paths]) - res = [p for p in paths if len(p) == min_len] - return res + If hyperedge_b is None, this returns the shortest paths from A to all others. + :param h: ASH hypergraph instance. + :param s: Minimum overlap size. + :param hyperedge_a: Starting hyperedge ID. + :param hyperedge_b: Ending hyperedge ID (optional). + :param start: Start time bound (inclusive). + :param end: End time bound (inclusive). + :param cutoff: Maximum path length. -def all_shortest_s_path( - h: ASH, s: int, hyperedge_a: str = None, start: int = None, end: int = None -) -> dict: + :return: List of shortest paths, each as list of IDs. """ + paths = list(all_simple_paths(h, s, hyperedge_a, hyperedge_b, start, end, cutoff)) + if not paths: + return [] + min_len = min(len(p) for p in paths) + return [p for p in paths if len(p) == min_len] + - :param h: - :param s: - :param hyperedge_a: - :param start: - :param end: - :return: +def all_shortest_s_paths( + h: ASH, + s: int, + hyperedge_a: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, + cutoff: Optional[int] = None, +) -> Dict[Tuple[str, str], List[List[str]]]: """ + Compute shortest s-paths for all hyperedge pairs (or from a source). - res = defaultdict(list) - for he in h.hyperedge_id_iterator(start, end): - if hyperedge_a is not None: - if he != hyperedge_a: - paths = list(all_simple_paths(h, s, hyperedge_a, he, start, end)) - min_len = min([len(p) for p in paths]) - res[(hyperedge_a, he)] = [p for p in paths if len(p) == min_len] - else: - for he1 in h.hyperedge_id_iterator(start, end): - if he != he1: - paths = list(all_simple_paths(h, s, he, he1, start, end)) - min_len = min([len(p) for p in paths]) - res[he, he1] = [p for p in paths if len(p) == min_len] - return res + When hyperedge_a is given, returns shortest paths from that source to all + other hyperedges. Otherwise, returns shortest paths for every unordered + pair, keyed both ways for convenience. + :param h: ASH hypergraph instance. + :param s: Minimum overlap size. + :param hyperedge_a: Source hyperedge ID (optional). + :param start: Start time bound (inclusive). + :param end: End time bound (inclusive). + :param cutoff: Maximum path length. -def all_shortest_s_path_length( - h: ASH, s: int, hyperedge_a: str = None, start: int = None, end: int = None -) -> dict: + :return: Dict mapping (u,v) to list of shortest paths. """ - - :param h: - :param s: - :param hyperedge_a: - :param start: - :param end: - :return: + result: Dict[Tuple[str, str], List[List[str]]] = defaultdict(list) + hyperedges = list(h.hyperedges(start, end)) + + if hyperedge_a: + # From one source to all others + for he in hyperedges: + if he == hyperedge_a: + continue + paths = list(all_simple_paths(h, s, hyperedge_a, he, start, end, cutoff)) + if not paths: + continue + min_len = min(len(p) for p in paths) + result[(hyperedge_a, he)] = [p for p in paths if len(p) == min_len] + else: + # Pairwise between all + for i, u in enumerate(hyperedges): + for v in hyperedges[i + 1 :]: + paths = list(all_simple_paths(h, s, u, v, start, end, cutoff)) + if not paths: + continue + min_len = min(len(p) for p in paths) + best = [p for p in paths if len(p) == min_len] + result[(u, v)] = best + result[(v, u)] = [list(reversed(p)) for p in best] + return result + + +def all_shortest_s_path_lengths( + h: ASH, + s: int, + hyperedge_a: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, + cutoff: Optional[int] = None, +) -> Dict[str, Dict[str, int]]: """ + Compute lengths of shortest s-overlap paths between hyperedges. - res = defaultdict(lambda: defaultdict(int)) - for he in h.hyperedge_id_iterator(start, end): - if hyperedge_a is not None: - if he != hyperedge_a: - paths = list(all_simple_paths(h, s, hyperedge_a, he, start, end)) - res[hyperedge_a][he] = min([len(p) for p in paths]) - 1 - res[he][hyperedge_a] = min([len(p) for p in paths]) - 1 - else: - res[hyperedge_a][he] = 0 - res[he][hyperedge_a] = 0 - else: - for he1 in h.hyperedge_id_iterator(start, end): - if he != he1: - paths = list(all_simple_paths(h, s, he, he1, start, end)) - res[he][he1] = min([len(p) for p in paths]) - 1 - res[he1][he] = min([len(p) for p in paths]) - 1 - else: - res[he1][he] = 0 - res[he][he1] = 0 - return res - - -def all_shortest_s_walk( - h: ASH, s: int, hyperedge_a: str = None, start: int = None, end: int = None -) -> dict: + When hyperedge_a is provided, returns dict lengths from source to others; + otherwise returns full matrix mapping each hyperedge to every other. + + :param h: ASH hypergraph instance. + :param s: Minimum overlap size. + :param hyperedge_a: Source hyperedge ID (optional). + :param start: Start time bound (inclusive). + :param end: End time bound (inclusive). + :param cutoff: Maximum path length. + + :return: Nested dict of distances (number of edges). """ + result: Dict[str, Dict[str, int]] = defaultdict(lambda: defaultdict(int)) + hyperedges = list(h.hyperedges(start, end)) + + if hyperedge_a: + # Distances from source + for he in hyperedges: + if he == hyperedge_a: + result[hyperedge_a][he] = 0 + continue + paths = list(all_simple_paths(h, s, hyperedge_a, he, start, end, cutoff)) + if paths: + length = min(len(p) for p in paths) - 1 + result[hyperedge_a][he] = length + result[he][hyperedge_a] = length + else: + # Full pairwise + for i, u in enumerate(hyperedges): + result[u][u] = 0 + for v in hyperedges[i + 1 :]: + paths = list(all_simple_paths(h, s, u, v, start, end, cutoff)) + if paths: + length = min(len(p) for p in paths) - 1 + result[u][v] = length + result[v][u] = length + return result + + +def all_shortest_s_walks( + h: ASH, + s: int, + hyperedge_a: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, + weight: bool = False, + edge: bool = True, +) -> Union[List[str], Dict[str, List[str]]]: + """ + Retrieve the shortest s-walk(s) in the hypergraph or its dual. + + Delegates to shortest_s_walk. + + :param h: ASH instance. + :param s: Minimum overlap size. + :param hyperedge_a: Source hyperedge ID (optional). + :param start: Start time bound. + :param end: End time bound. - :param h: - :param s: - :param hyperedge_a: - :param start: - :param end: - :return: + :return: Single path (list) if two endpoints specified, or dict of + {target: path} if one endpoint, or nested dict if neither. """ - return shortest_s_walk(h, s, hyperedge_a, start, end) + return shortest_s_walk(h, s, hyperedge_a, None, start, end, weight, edge) -def all_shortest_s_walk_length( - h: ASH, s: int, hyperedge_a: str = None, start: int = None, end: int = None -) -> dict: + +def all_shortest_s_walk_lengths( + h: ASH, + s: int, + hyperedge_a: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, +) -> Dict[str, Dict[str, int]]: """ + Compute lengths of shortest s-walks between hyperedges. - :param h: - :param s: - :param hyperedge_a: - :param start: - :param end: - :return: + :param h: ASH instance. + :param s: Minimum overlap size. + :param hyperedge_a: Source hyperedge ID (optional). + :param start: Start time bound. + :param end: End time bound. + + :return: Nested dict mapping hyperedge to target to length. """ - res = {} - walks = all_shortest_s_walk(h, s, hyperedge_a, start, end) - for k, v in walks.items(): - if hyperedge_a not in res: - res[hyperedge_a] = {k: len(v)} - else: - res[hyperedge_a][k] = len(v) - res[k] = {hyperedge_a: len(v)} - return res + walks = all_shortest_s_walks(h, s, hyperedge_a, start, end) + lengths: Dict[str, Dict[str, int]] = {} + # walks may be dict or list + if isinstance(walks, dict): + for tgt, path in walks.items(): + lengths.setdefault(hyperedge_a, {})[tgt] = len(path) + lengths.setdefault(tgt, {})[hyperedge_a] = len(path) + return lengths def shortest_s_walk( h: ASH, s: int, - fr: str = None, - to: str = None, - start: int = None, - end: int = None, + fr: Optional[str] = None, + to: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, weight: bool = False, edge: bool = True, -) -> object: - """ - All returned paths include both the source and target in the path. - - If the source and target are both specified, return a single list of nodes in - a shortest path from the source to the target. - If only the source is specified, return a dictionary keyed by targets with a - list of nodes in a shortest path from the source to one of the targets. - If only the target is specified, return a dictionary keyed by sources with a - list of nodes in a shortest path from one of the sources to the target. - If neither the source nor target are specified return a dictionary of dictionaries - with path[source][target]=[list of nodes in path]. - - - :param h: - :param s: - :param fr: - :param to: - :param start: - :param end: - :param weight: - :param edge: - :return: +) -> Union[List[str], Dict[str, List[str]]]: """ + Compute shortest s-walk(s) considering weight or dual hypergraph. + If edge=True, operates on s-line-graph; otherwise uses dual hypergraph node graph. + + :param h: ASH instance. + :param s: Minimum overlap size. + :param fr: Starting hyperedge ID (node or edge depending). + :param to: Ending hyperedge ID. + :param start: Start time bound. + :param end: End time bound. + :param weight: Use edge weight attribute 'w' if True. + :param edge: If False, compute on dual hypergraph. + + :return: Single path list if both fr and to set, else dict mapping. + """ + # Build appropriate graph if edge: g = h.s_line_graph(s, start, end) + # Guards for explicit endpoints + if (fr is not None and fr not in g) or (to is not None and to not in g): + return [] if (fr is not None and to is not None) else {} + + # Case 1: specific source and target -> single path as list if fr is not None and to is not None: - if not g.has_node(fr) or not g.has_node(to): - return [] - elif fr is not None and not g.has_node(fr): - return [] + return nx.shortest_path( + g, source=fr, target=to, weight="w" if weight else None + ) - if weight: - return nx.shortest_path(g, source=fr, target=to, weight="w") - return nx.shortest_path(g, source=fr, target=to) + # Case 2: specific source only -> dict {target: path} + if fr is not None: + if weight: + return nx.single_source_dijkstra_path(g, fr, weight="w") + return nx.single_source_shortest_path(g, fr) + # Case 3: no endpoints -> dict {source: {target: path}} + if weight: + pairs_iter = nx.all_pairs_dijkstra_path(g, weight="w") + else: + pairs_iter = nx.all_pairs_shortest_path(g) + # Materialize iterator (NetworkX >=3.3 returns iterator for all-pairs) + return {src: tgt_paths for src, tgt_paths in pairs_iter} else: + # Dual graph handling h1, node_to_eid = h.dual_hypergraph(start=start, end=end) - eid_to_node = {v: k for k, v in node_to_eid.items()} - - eid1, eid2 = fr, to - if fr is not None: - eid1 = node_to_eid[fr] - if to is not None: - eid2 = node_to_eid[to] - - res = shortest_s_walk(h1, s, eid1, eid2, weight=weight) - out = {} - if isinstance(res, dict): - for k, v in res.items(): - out[eid_to_node[k]] = [eid_to_node[i] for i in v] - return out - else: - return [eid_to_node[i] for i in res] + eid_to_node = {eid: node for node, eid in node_to_eid.items()} + # map fr/to to dual nodes + src = node_to_eid.get(fr, fr) + dst = node_to_eid.get(to, to) + raw = shortest_s_walk(h1, s, src, dst, start, end, weight, edge=True) + # remap back + if isinstance(raw, dict): + return { + eid_to_node[k]: [eid_to_node[n] for n in path] + for k, path in raw.items() + } + return [eid_to_node[n] for n in raw] def closed_s_walk( - h: ASH, s: int, hyperedge_a: str = None, start: int = None, end: int = None -) -> object: + h: ASH, + s: int, + hyperedge_a: str, + start: Optional[int] = None, + end: Optional[int] = None, +) -> List[List[str]]: """ + Find all simple cycles (basis) in the s-line-graph containing a given node. + + :param h: ASH instance. + :param s: Minimum overlap size. + :param hyperedge_a: Node ID in s-line-graph to find cycles through. + :param start: Start time bound. + :param end: End time bound. - :param h: - :param s: - :param hyperedge_a: - :param start: - :param end: - :return: + :return: List of cycles, each as list of hyperedge IDs. """ g = h.s_line_graph(s, start, end) - - if not g.has_node(hyperedge_a): + if hyperedge_a not in g: return [] return nx.cycle_basis(g, hyperedge_a) @@ -255,82 +338,121 @@ def closed_s_walk( def s_distance( h: ASH, s: int, - fr: str = None, - to: str = None, - start: int = None, - end: int = None, + fr: Optional[str] = None, + to: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, weight: bool = False, edge: bool = True, -) -> object: +) -> Union[int, Dict[str, Dict[str, int]], None]: """ - - :param h: - :param s: - :param fr: - :param to: - :param start: - :param end: - :param weight: - :param edge: - :return: + Compute shortest-path distances in s-line-graph or dual hypergraph. + If edge=True, uses s-line-graph; otherwise uses dual hypergraph. + + :param h: ASH instance. + :param s: Minimum overlap size. + :param fr: Source ID. + :param to: Target ID. + :param start: Start time bound. + :param end: End time bound. + :param weight: Use edge weight attribute 'w' if True. + :param edge: If False, use dual hypergraph distances. + + :return: Single distance, nested dict of distances, or None if unreachable. """ - if edge: - g = h.s_line_graph(s, start, end) - - if fr is not None and to is not None: - if not g.has_node(fr) or not g.has_node(to): - return None - elif fr is not None and not g.has_node(fr): + G = h.s_line_graph(s, start, end) + # guard: if either endpoint is missing, bail + if (fr and fr not in G) or (to and to not in G): return None - - if weight: - return nx.shortest_path_length(g, source=fr, target=to, weight="w") - return nx.shortest_path_length(g, source=fr, target=to) - + # pick the right algorithm + if fr and to: + return nx.shortest_path_length( + G, source=fr, target=to, weight="w" if weight else None + ) + elif fr: + # distances from fr to all reachable nodes + return nx.single_source_dijkstra_path_length( + G, fr, weight="w" if weight else None + ) + else: + # distances from fr to all reachable nodes + return { + fr: nx.single_source_dijkstra_path_length( + G, fr, weight="w" if weight else None + ) + for fr in G.nodes() + } else: - h1, node_to_eid = h.dual_hypergraph(start=start, end=end) - eid_to_node = {v: k for k, v in node_to_eid.items()} - eid1, eid2 = fr, to - if fr is not None: - eid1 = node_to_eid[fr] - if to is not None: - eid2 = node_to_eid[to] - - res = s_distance(h1, s, eid1, eid2, weight=weight) - if isinstance(res, int): - return res - elif isinstance(res, dict): - return {eid_to_node[k]: v for k, v in res.items()} - elif res is None: + # build dual and invert its node‐to‐eid map + H_dual, node_to_eid = h.dual_hypergraph( + start=start, end=end + ) # node represent hyperedges + eid_to_node = { + eid: node for node, eid in node_to_eid.items() + } # maps projected hyperedges to real nodes + # while node_to_eid maps real nodes to projected hyperedges + + # translate your fr/to into the dual graph’s hyperedges + src = node_to_eid.get(fr, fr) + dst = node_to_eid.get(to, to) + + # compute distances on the dual graph + dual_res = s_distance( + H_dual, s, fr=src, to=dst, start=start, end=end, edge=True, weight=weight + ) + # raise ValueError(f"{dual_res}, {src}, {dst}") + if dual_res is None: return None - else: - res = list(res) - out = [] - for n, d in res: - out.append((eid_to_node[n], {eid_to_node[k]: v for k, v in d.items()})) - return out + + # if it’s a single integer, map back and return + if isinstance(dual_res, int): + return dual_res + + # if it's a nested dict, map it back + if isinstance(dual_res, dict) and any( + isinstance(v, dict) for v in dual_res.values() + ): + remapped: Dict[str, Dict[str, int]] = {} + for dual_src, targets in dual_res.items(): + src = eid_to_node.get(dual_src, dual_src) + remapped[src] = {} + for dual_trg, dist in targets.items(): + trg = eid_to_node.get(dual_trg, dual_trg) + remapped[src][trg] = dist + return remapped + + # else it must be a normal dict + remapped: Dict[str, int] = {} + for dual_trg, dist in dual_res.items(): + # remap the target hyperedge ID + trg = eid_to_node.get(dual_trg, dual_trg) + # remap the source hyperedge IDs + remapped[trg] = dist + print(f"remapped: {remapped}") + return remapped def average_s_distance( h: ASH, s: int, - start: int = None, - end: int = None, + start: Optional[int] = None, + end: Optional[int] = None, weight: bool = False, - edge: bool = False, + edge: bool = True, ) -> float: """ + Compute the average shortest-path length in the s-line-graph. - :param h: - :param s: - :param start: - :param end: - :param weight: - :param edge: - :return: - """ + :param h: ASH instance. + :param s: Minimum overlap size. + :param start: Start time bound. + :param end: End time bound. + :param weight: Use edge weight attribute 'w' if True (unused here). + :param edge: (Unused) Included for API consistency. + :return: Average distance across all connected pairs. + """ if not edge: h, _ = h.dual_hypergraph(start=start, end=end) @@ -344,122 +466,121 @@ def average_s_distance( def has_s_walk( h: ASH, s: int, - fr: str = None, - to: str = None, - start: int = None, - end: int = None, + fr: Optional[str] = None, + to: Optional[str] = None, + start: Optional[int] = None, + end: Optional[int] = None, edge: bool = True, ) -> bool: """ + Determine if an s-overlap walk exists between two hyperedges. - :param h: - :param s: - :param fr: - :param to: - :param start: - :param end: - :param edge: - :return: - """ - - if not edge: - h, node_to_eid = h.dual_hypergraph(start=start, end=end) - - if fr is not None: - fr = node_to_eid[fr] - if to is not None: - to = node_to_eid[to] - - g = h.s_line_graph(s, start, end) + :param h: ASH instance. + :param s: Minimum overlap size. + :param fr: Source hyperedge ID. + :param to: Target hyperedge ID. + :param start: Start time bound. + :param end: End time bound. + :param edge: If False, evaluate on dual hypergraph. - if fr is not None and to is not None: - if not g.has_node(fr) or not g.has_node(to): + :return: True if a path exists, False otherwise. + """ + if edge: + g = h.s_line_graph(s, start, end) + if fr and fr not in g or to and to not in g: return False - elif fr is not None and not g.has_node(fr): - return False - - return nx.has_path(g, fr, to) + return nx.has_path(g, fr, to) + else: + h1, node_to_eid = h.dual_hypergraph(start=start, end=end) + src = node_to_eid.get(fr, fr) + dst = node_to_eid.get(to, to) + return has_s_walk(h1, s, src, dst, start, end, edge=True) def s_diameter( h: ASH, s: int, - start: int = None, - end: int = None, + start: Optional[int] = None, + end: Optional[int] = None, weight: bool = False, - edge: bool = False, + edge: bool = True, ) -> int: """ + Compute the diameter (longest shortest-path) of the s-line-graph. + + :param h: ASH instance. + :param s: Minimum overlap size. + :param start: Start time bound. + :param end: End time bound. + :param weight: Use weighted distances if True. + :param edge: If False, compute on dual hypergraph. - :param h: - :param s: - :param start: - :param end: - :param weight: - :param edge: - :return: + :return: Integer diameter of the graph (0 if empty). """ if not edge: h, _ = h.dual_hypergraph(start=start, end=end) - - distances = s_distance(h, s, start=start, end=end, weight=weight) - diameter = 0 - for _, data in dict(distances).items(): - for _, dist in data.items(): - if diameter < dist: - diameter = dist - - return diameter + g = h.s_line_graph(s, start, end) + # lcc + comps = list(nx.connected_components(g)) + lcc = max(comps, key=len) if comps else set() + lcc = g.subgraph(lcc) + diam = nx.diameter(lcc, weight="w" if weight else None) + return diam if diam is not None else 0 def s_components( - h: ASH, s: int, start: int = None, end: int = None, edge: bool = True -) -> list: + h: ASH, + s: int, + start: Optional[int] = None, + end: Optional[int] = None, + edge: bool = True, +) -> Iterator[set]: """ + Yield connected components of the s-line-graph or its dual. + + :param h: ASH instance. + :param s: Minimum overlap size. + :param start: Start time bound. + :param end: End time bound. + :param edge: If False, yields on dual hypergraph components. - :param h: - :param s: - :param start: - :param end: - :param edge: - :return: + :return: Iterator of sets of hyperedge IDs per component. """ if edge: g = h.s_line_graph(s, start, end) - for comp in nx.connected_components(g): - yield comp - + yield from nx.connected_components(g) else: h1, node_to_eid = h.dual_hypergraph(start=start, end=end) - eid_to_node = {v: k for k, v in node_to_eid.items()} + translate = {eid: node for node, eid in node_to_eid.items()} + # iterate over components in the dual graph + for comp in s_components(h1, s, start, end, edge=True): + yield {translate[eid] for eid in comp} - for comp in s_components(h1, s): - yield {eid_to_node[i] for i in comp} +def is_s_path(h: ASH, walk: List[str]) -> bool: + """Validate that a hyperedge sequence is a simple s-path. -def is_s_path(h: ASH, walk: list) -> bool: - """ - The is_s_path function takes in an ASH instance and a list of nodes, which represents - a walk through the hypergraph. The function returns True if the walk is an s-path, - and False otherwise. + A simple s-path here means: - :param h: ASH instance - :param walk: The sequence of nodes - :return: True if the given walk is an s-path, and false otherwise + * No hyperedge appears more than once in the sequence. + * No node participates in overlaps between more than two hyperedges (prevents reuse of the same node in non-consecutive steps). + :param h: ASH instance + :param walk: List of hyperedge IDs forming the candidate path + :return: True if valid s-path, False otherwise """ - - p = Counter(walk) - if max(p.values()) > 1: + # Check for repeated hyperedges + if any(count > 1 for count in Counter(walk).values()): return False - res = [] + # Collect all node overlaps between any two hyperedges in the walk + node_counts: Counter = Counter() for u, v in combinations(walk, 2): - intersect = set(h.get_hyperedge_nodes(u)) & set(h.get_hyperedge_nodes(v)) - res.extend(list(intersect)) + nodes_u = set(h.get_hyperedge_nodes(u)) + nodes_v = set(h.get_hyperedge_nodes(v)) + node_counts.update(nodes_u & nodes_v) - p = Counter(res) - if max(p.values()) > 1: + # If any node appears in more than one overlap, path is not simple + if any(count > 1 for count in node_counts.values()): return False - else: - return True + return True diff --git a/ash_model/readwrite/io.py b/ash_model/readwrite/io.py index 9415e32..d6ddef5 100644 --- a/ash_model/readwrite/io.py +++ b/ash_model/readwrite/io.py @@ -1,5 +1,7 @@ import gzip import json +from collections import defaultdict +from typing import List, Dict, Tuple, Any, Optional from ash_model import ASH, NProfile @@ -12,6 +14,8 @@ "read_sh_from_csv", "write_ash_to_json", "read_ash_from_json", + "write_hif", + "read_hif", ] @@ -25,6 +29,7 @@ def __write_profile_to_csv( :param path: :param delimiter: :param append: + :return: """ @@ -34,34 +39,30 @@ def __write_profile_to_csv( op = open(path, "w") with op as f: - for tid in h.get_node_presence(node): + for tid in h.node_presence(node): res = f"{node}{delimiter}{tid}" profiles = h.get_node_profile(node, tid) descr = profiles.get_attributes() - for k in sorted(descr): + for k in sorted(descr.keys()): res = f"{res}{delimiter}{descr[k]}" f.write(f"{res}\n") def write_profiles_to_csv(h: ASH, path: str, delimiter: str = ",") -> None: """ - Writes node profiles data in CSV format. Each row is a profile at a specific temporal id, with the corresponding - attributes in that tid - :param h: ASH instance - :param path: file path to save to - :param delimiter: column delimiter + :param h: + :param path: + :param delimiter: + :return: """ head = True - for node in h.node_iterator(): + for node in h.nodes(): if head: - prof = h.get_node_profile(node) - heads = list(prof.get_attributes().keys()) - heads.remove("t") - heads = f"{delimiter}".join(sorted(heads)) - head = f"node_id,tid,{heads}\n" + heads = delimiter.join(sorted(h.list_node_attributes().keys())) + head = f"node_id{delimiter}tid{delimiter}{heads}\n" with open(path, "w") as f: f.write(head) @@ -72,20 +73,30 @@ def write_profiles_to_csv(h: ASH, path: str, delimiter: str = ",") -> None: def read_profiles_from_csv(path: str, delimiter: str = ",") -> dict: """ - Reads node profiles data from CSV format into a dictionary. - Each row must be a profile at a specific temporal id, with the corresponding attributes in that tid - :param path: file path to read from - :param delimiter: column delimiter + :param path: + :param delimiter: + :return: """ res = {} + with open(path, "r") as f: + # readl all + x = f.readlines() + print(x) with open(path) as f: head = f.readline().rstrip().split(delimiter) for row in f: row = row.rstrip().split(delimiter) prof = {head[i]: row[i] for i in range(2, len(row))} + # convert types + for k, v in prof.items(): + if v.isdigit(): + prof[k] = int(v) + elif v.replace(".", "", 1).isdigit(): + prof[k] = float(v) + # else keep as string if int(row[0]) not in res: res[int(row[0])] = {int(row[1]): NProfile(node_id=int(row[0]), **prof)} else: @@ -103,11 +114,12 @@ def __write_profile_to_json( :param path: :param compress: :param append: + :return: """ js_dmp = profile.to_dict() - js_dmp["t"] = tid + js_dmp["tid"] = tid if compress: op = gzip.open @@ -124,26 +136,28 @@ def __write_profile_to_json( def write_profiles_to_jsonl(a: ASH, path: str, compress: bool = False) -> None: """ - Write each NProfile as a JSON string, one per line. - :param a: ASH instance - :param path: file path to save to - :param compress: whether to use file compression + :param a: + :param path: + :param compress: + :return: """ - for node in a.node_iterator(): - for tid in a.get_node_presence(node): + for node in a.nodes(): + for tid in a.node_presence(node): profile = a.get_node_profile(node, tid) __write_profile_to_json(profile, tid, path, compress, append=True) def read_profiles_from_jsonl(path: str, compress: bool = False) -> dict: """ - Reads NProfiles from a file where each line contain a JSON string representing the profile. + Read a dictionary of node profiles from a JSONL file. + The dictionary maps node IDs to dictionaries of timestamps to node profiles. + + :param path: Path to the JSONL file. + :param compress: If True, the file is assumed to be compressed using gzip. - :param path: file path to read from - :param compress: whether the file is compressed - :return: a dictionary containing node profiles + :return: Dictionary of node profiles. """ if compress: op = gzip.open @@ -153,66 +167,71 @@ def read_profiles_from_jsonl(path: str, compress: bool = False) -> dict: res = {} with op(path) as f: for l in f: - rep = json.loads(l) - - if rep["node_id"] not in res: - res[rep["node_id"]] = { - rep["t"]: NProfile(rep["node_id"], **rep["attrs"]) - } - else: - res[rep["node_id"]][rep["t"]] = NProfile(rep["node_id"], **rep["attrs"]) + data = json.loads(l) + node_id = data["node_id"] + tid = data["tid"] + del data["node_id"] + del data["tid"] + res.setdefault(node_id, {})[tid] = NProfile(node_id=node_id, **data) return res def write_sh_to_csv(h: ASH, path: str) -> None: """ - Writes interactions to CSV format. Each row identifies a hyperedge; - the first column contains hyperedge nodes, the second contains start-end temporal ids, - :param h: ASH instance - :param path: file path to write to - :return: + Write a list of timestamped hyperedges to a CSV file. + Does not support attributes. + The CSV file will have the following format: + n1,n2,...\tstart,end + Warning: there is no guarantee that the order of hyperedges will be preserved when reading back. + + :param h: ASH object to write. + :param path: Path to the CSV file. + + :return: None """ with open(path, "w") as o: o.write("nodes\tstart,end\n") - for he in h.hyperedge_id_iterator(): - attrs = h.get_hyperedge_attributes(he) - for span in attrs["t"]: - nodes = [str(n) for n in attrs["nodes"]] - desc = ",".join(nodes) + for he in h.hyperedges(): + presence = h.hyperedge_presence(he, as_intervals=True) + nodes = h.get_hyperedge_nodes(he) + for span in presence: + desc = ",".join([str(n) for n in nodes]) desc = f"{desc}\t{span[0]},{span[1]}\n" o.write(desc) def read_sh_from_csv(path: str) -> ASH: """ - Read interactions from CSV format. Each row must identify a hyperedge; - the first column must contain hyperedge nodes, the second must contain start-end temporal ids, + Read a list of timestamped hyperedges from a CSV file. + Does not support attributes. + Warning: there is no guarantee that the order of hyperedges will be preserved. - :param path: file path to write to - :return: ASH instance - """ + :param path: Path to the CSV file. - a = ASH(hedge_removal=True) + :return: + """ + a = ASH() with open(path) as f: _ = f.readline() for row in f: nodes, span = row.rstrip().split("\t") nodes = [int(n) for n in nodes.split(",")] - span = [int(t) for t in span.split(",")] + span = [int(s) for s in span.split(",")] a.add_hyperedge(nodes, start=span[0], end=span[1]) return a def write_ash_to_json(h: ASH, path: str, compress: bool = False) -> None: """ - Write ASH instance to JSON object. Keys are 'nodes' for node profiles and 'hedges' for interactions + Write an ASH object to a JSON file. - :param h: ASH instance - :param path: file path to write to - :param compress: whether to use file compression - :return: + :param h: ASH object to write. + :param path: Path to the JSON file. + :param compress: If True, the file will be compressed using gzip. + + :return: None """ js_dmp = json.dumps(h.to_dict(), indent=2) @@ -227,13 +246,14 @@ def write_ash_to_json(h: ASH, path: str, compress: bool = False) -> None: def read_ash_from_json(path: str, compress: bool = False) -> ASH: """ - Read ASH instance from JSON file. Keys must be 'nodes' for node profiles 'hedges' for interactions + Read an ASH object from a JSON file. - :param path: file path to read from - :param compress: whether the file is compressed - :return: + :param path: Path to the JSON file. + :param compress: If True, the file is assumed to be compressed using gzip. + + :return: ASH object """ - h = ASH(hedge_removal=True) + h = ASH() if compress: op = gzip.open @@ -243,32 +263,230 @@ def read_ash_from_json(path: str, compress: bool = False) -> ASH: with op(path, "rt") as f: data = json.loads(f.read()) - for _, v in data["hedges"].items(): - nodes = v["nodes"] - spans = v["t"] - for span in spans: - h.add_hyperedge(nodes, start=span[0], end=span[1]) + # Add nodes + attrs = defaultdict(lambda: defaultdict(dict)) + for node_id, node_data in data["nodes"].items(): + for tid, attr in node_data.items(): + attrs[int(node_id)][int(tid)] = attr + h._node_attrs = attrs + + for _, edge_data in data["hedges"].items(): + for span in edge_data["attributes"]["_presence"]: + for t in range(span[0], span[1] + 1): + + kwargs = { + k: v for k, v in edge_data["attributes"].items() if k != "_presence" + } + + h.add_hyperedge(edge_data["nodes"], start=t, **kwargs) + + return h - for nid, attrs in data["nodes"].items(): - nid = int(nid) - spans = attrs["t"] - for span in spans: - h.add_node(nid, span[0], span[1]) - keys = list(attrs.keys()) - keys.remove("t") +def __to_hif(h: ASH, metadata: Optional[Dict[str, Any]] = None) -> None: + + hif: Dict[str, Any] = {} + hif["network-type"] = "undirected" + if metadata is not None: + hif["metadata"] = metadata + + # --- Incidences: one record per node–edge membership ------------- + incidences: List[Dict[str, Any]] = [] + for hid in h.hyperedges(): + weight = h.get_hyperedge_weight(hid) + for n in h.get_hyperedge_nodes(hid): + rec = {"node": n, "edge": hid} + if weight != 1: + rec["weight"] = weight + incidences.append(rec) + hif["incidences"] = incidences + + # --- Nodes: include time‐varying attrs as intervals --------------- + nodes_list: List[Dict[str, Any]] = [] + # first, get full set of node‐attr names + all_node_attrs = set(h.list_node_attributes().keys()) + for n in h.nodes(): + attrs: Dict[str, Any] = {} + # for each attr, build list of (start, end, value) intervals + for attr in all_node_attrs: + time_values = h.get_node_attribute(n, attr) # {t: value} + if not any(v is not None for v in time_values.values()): + continue + # collapse into contiguous spans with same value + times = sorted(time_values.keys()) + spans: List[Tuple[int, int, Any]] = [] + s = times[0] + e = s + cur = time_values[s] + for t in times[1:]: + v = time_values[t] + if v == cur and t == e + 1: + e = t + else: + spans.append((s, e, cur)) + s, e, cur = t, t, v + spans.append((s, e, cur)) + attrs[attr] = spans + # also include node presence intervals explicitly + attrs["_presence"] = h.node_presence(n, as_intervals=True) + nodes_list.append({"node": n, "attrs": attrs}) + hif["nodes"] = nodes_list + + # --- Edges: existing attrs + temporal presence ------------------ + edges_list: List[Dict[str, Any]] = [] + for hid in h.hyperedges(): + attrs = dict(h.get_hyperedge_attributes(hid)) + # embed temporal presence as intervals + attrs["_presence"] = h.hyperedge_presence(hid, as_intervals=True) # type: ignore[arg-type] + edges_list.append({"edge": hid, "attrs": attrs}) + hif["edges"] = edges_list + + return hif + + +def __from_hif(data: dict) -> ASH: + """ + Convert HIF data dictionary to ASH object. - t_to_values = {} + :param data: Dictionary containing HIF data - for key in keys: - values = attrs[key] - for t, v in values.items(): - if t in t_to_values: - t_to_values[t][key] = v + :return: ASH object + """ + h = ASH() + + if data.get("network-type") != "undirected": + raise NotImplementedError("Only undirected hypernetworks are supported.") + + # Process nodes and their attributes + if "nodes" in data: + for node_data in data["nodes"]: + node_id = node_data["node"] + attrs = node_data.get("attrs", {}) + + # Choose a reference time for static attributes: + # prefer the start of the first presence interval, else 0 + t0 = 0 + presence_intervals = attrs.get("_presence", []) + if isinstance(presence_intervals, list) and len(presence_intervals) > 0: + first = presence_intervals[0] + if isinstance(first, (list, tuple)) and len(first) == 2: + try: + t0 = int(first[0]) + except Exception: + t0 = 0 + elif isinstance(first, (int,)): + t0 = int(first) + + # Process each attribute (except _presence which is handled separately) + for attr_name, spec in attrs.items(): + if attr_name == "_presence": + continue # Skip presence; node presence is implied by attrs/edges + + # Case 1: temporal attribute encoded as list of (start, end, value) + if isinstance(spec, list) and all( + isinstance(x, (list, tuple)) and len(x) == 3 for x in spec + ): + for start, end, value in spec: + # for each t in the closed interval [start, end] + for t in range(int(start), int(end) + 1): + if not hasattr(h, "_node_attrs"): + h._node_attrs = defaultdict(lambda: defaultdict(dict)) + h._node_attrs[node_id][t][attr_name] = value + else: + # Case 2: static attribute -> assign at a single time instant t0 + if not hasattr(h, "_node_attrs"): + h._node_attrs = defaultdict(lambda: defaultdict(dict)) + h._node_attrs[node_id][t0][attr_name] = spec + + # Process hyperedges + if "edges" in data: + for edge_data in data["edges"]: + edge_id = edge_data["edge"] + attrs = edge_data.get("attrs", {}) + + # Get presence specification and normalize to list of (start,end) + presence_spec = attrs.get("_presence", None) + presence_intervals: List[Tuple[int, int]] = [] + if presence_spec is None or ( + isinstance(presence_spec, list) and len(presence_spec) == 0 + ): + # No presence provided -> treat as static at t=0 + presence_intervals = [(0, 0)] + elif isinstance(presence_spec, list): + # Allow either list of intervals or list of instants + if all( + isinstance(x, (list, tuple)) and len(x) == 2 for x in presence_spec + ): + presence_intervals = [(int(s), int(e)) for s, e in presence_spec] # type: ignore[misc] + elif all(isinstance(x, (int,)) for x in presence_spec): + presence_intervals = [(int(t), int(t)) for t in presence_spec] # type: ignore[misc] else: - t_to_values[t] = {key: v} + # Fallback: treat as static at t=0 + presence_intervals = [(0, 0)] + else: + # Unexpected type -> default to static at t=0 + presence_intervals = [(0, 0)] + + # Get other attributes (excluding _presence) + edge_attrs = {k: v for k, v in attrs.items() if k != "_presence"} + + # We need to get the nodes for this edge from incidences + edge_nodes = [] + if "incidences" in data: + edge_nodes = [ + inc["node"] for inc in data["incidences"] if inc["edge"] == edge_id + ] + # Remove duplicates while preserving order + seen = set() + edge_nodes = [x for x in edge_nodes if not (x in seen or seen.add(x))] + + # Add hyperedge for each presence interval + for start, end in presence_intervals: + h.add_hyperedge(edge_nodes, start=start, end=end, **edge_attrs) + + return h + + +def write_hif( + h: ASH, path: str, metadata: Optional[Dict[str, Any]] = None, compress: bool = False +) -> None: + """ + Write an ASH object to a HIF file. + + :param h: ASH object to write. + :param path: Path to the HIF file. + :param compress: If True, the file will be compressed using gzip. + + :return: None + """ + hif = __to_hif(h, metadata) + + if compress: + op = gzip.open + else: + op = open + + with op(path, "wt") as f: + json.dump(hif, f, indent=2) + + +def read_hif(path: str, compress: bool = False) -> ASH: + """ + Read an ASH object from a HIF file. + + :param path: Path to the HIF file. + :param compress: If True, the file is assumed to be compressed using gzip. + + :return: ASH object + """ + if compress: + op = gzip.open + else: + op = open + + with op(path, "rt") as f: + data = json.loads(f.read()) - for tid, prof in t_to_values.items(): - h.add_node(nid, int(tid), attr_dict=NProfile(node_id=nid, **prof)) + h = __from_hif(data) return h diff --git a/ash_model/test/conftest.py b/ash_model/test/conftest.py new file mode 100644 index 0000000..46d2437 --- /dev/null +++ b/ash_model/test/conftest.py @@ -0,0 +1,85 @@ +"""Pytest configuration and shared fixtures for ASH test suite.""" + +import pytest +import numpy as np +import warnings +import matplotlib + +matplotlib.use("Agg") # Non-interactive backend for testing + + +@pytest.fixture(autouse=True, scope="session") +def _configure_test_session(): + """ + Configurazione di sessione per i test: + - Forza backend matplotlib Agg (headless) + - Sopprime warning benigni noti dalle routine di viz + """ + try: + import matplotlib + + matplotlib.use("Agg", force=True) + except Exception: + # Non bloccare la suite se matplotlib non è presente + pass + + # Sopprimi warning noti: legend senza artists nelle figure di test + warnings.filterwarnings( + "ignore", + message=r"No artists with labels found to put in legend\.", + category=UserWarning, + ) + + +@pytest.fixture() +def rng() -> np.random.Generator: + """Generatore deterministico per test che richiedono random.""" + return np.random.default_rng(0) + + +@pytest.fixture() +def ash_factory(): + """Factory per creare istanze ASH con backend opzionale.""" + from ash_model import ASH + + def _make(backend: str | None = None) -> ASH: + return ASH() if backend is None else ASH(backend=backend) + + return _make + + +@pytest.fixture() +def small_hg(ash_factory): + """Piccolo ipergrafo statico di utilità.""" + a = ash_factory() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([15, 25], 0) + a.add_hyperedge([1, 24, 34], 0) + a.add_hyperedge([1, 2, 5, 6], 0) + a.add_hyperedge([1, 2, 5], 1) + a.add_hyperedge([3, 4, 5, 10], 1) + a.add_hyperedge([3, 4, 5, 12], 1) + return a + + +@pytest.fixture() +def small_temporal_hg(ash_factory): + """Piccolo ipergrafo temporale multi-snapshot.""" + a = ash_factory() + # e1: 1-2 attivo 0..2 + a.add_hyperedge([1, 2], 0, 2) + # e2: 2-3 attivo 1..3 + a.add_hyperedge([2, 3], 1, 3) + # e3: 3-4 attivo 3..3 + a.add_hyperedge([3, 4], 3, 3) + return a + + +@pytest.fixture() +def matplotlib_agg(): + """Ensure matplotlib uses non-interactive backend for tests.""" + import matplotlib.pyplot as plt + + yield + # Cleanup + plt.close("all") diff --git a/ash_model/test/fixtures/__init__.py b/ash_model/test/fixtures/__init__.py new file mode 100644 index 0000000..f28c198 --- /dev/null +++ b/ash_model/test/fixtures/__init__.py @@ -0,0 +1 @@ +"""Shared test fixtures and utilities for ASH test suite.""" diff --git a/ash_model/test/fixtures/sample_hypergraphs.py b/ash_model/test/fixtures/sample_hypergraphs.py new file mode 100644 index 0000000..cf5a924 --- /dev/null +++ b/ash_model/test/fixtures/sample_hypergraphs.py @@ -0,0 +1,83 @@ +"""Factory functions for creating sample hypergraphs used across tests.""" + +from ash_model import ASH, NProfile + + +def small_hypergraph(): + """Create a small hypergraph with 4 nodes and 2 hyperedges for basic testing.""" + h = ASH() + h.add_hyperedge([1, 2, 3], start=0) + h.add_hyperedge([2, 4], start=0) + return h + + +def temporal_hypergraph(): + """Create a hypergraph with temporal dynamics for time-based testing.""" + h = ASH() + h.add_hyperedge([1, 2, 3], start=0, end=4) # e1: t in [0,4] + h.add_hyperedge([1, 4], start=0, end=1) # e2: t in [0,1] + h.add_hyperedge([1, 2, 3, 4], start=2, end=3) # e3: t in [2,3] + h.add_hyperedge([1, 3, 4], start=2, end=3) # e4: t in [2,3] + h.add_hyperedge([3, 4], start=3, end=4) # e5: t in [3,4] + return h + + +def attributed_hypergraph(): + """Create a hypergraph with node attributes for testing attribute-based measures.""" + h = ASH() + + # Add nodes with attributes + h.add_node(1, start=0, end=2, attr_dict={"group": "A", "age": 25}) + h.add_node(2, start=0, end=2, attr_dict={"group": "A", "age": 30}) + h.add_node(3, start=0, end=2, attr_dict={"group": "B", "age": 35}) + h.add_node(4, start=0, end=2, attr_dict={"group": "B", "age": 40}) + + # Add hyperedges + h.add_hyperedge([1, 2], start=0) + h.add_hyperedge([2, 3], start=1) + h.add_hyperedge([3, 4], start=2) + h.add_hyperedge([1, 2, 3], start=1) + + return h + + +def dense_temporal_hypergraph(): + """Create a denser hypergraph for performance and stress testing.""" + h = ASH() + for t in range(10): + for i in range(1, 6): + nodes = list(range(i, min(i + 3, 11))) + h.add_hyperedge(nodes, start=t, end=t) + return h + + +def hypergraph_with_profiles(): + """Create a hypergraph with rich node profiles for profile testing.""" + h = ASH() + + profile1 = NProfile(node_id=1, name="Alice", department="CS", publications=10) + profile2 = NProfile(node_id=2, name="Bob", department="Math", publications=15) + profile3 = NProfile(node_id=3, name="Charlie", department="CS", publications=8) + + h.add_node(1, start=0, end=2, attr_dict=profile1) + h.add_node(2, start=0, end=2, attr_dict=profile2) + h.add_node(3, start=0, end=2, attr_dict=profile3) + + h.add_hyperedge([1, 2, 3], start=0) + h.add_hyperedge([1, 3], start=1) + h.add_hyperedge([2, 3], start=2) + + return h + + +def bipartite_hypergraph(): + """Create a bipartite hypergraph for projection testing.""" + h = ASH() + # Set A: nodes 1, 2, 3 + # Set B: nodes 4, 5, 6 + h.add_hyperedge([1, 4], start=0) + h.add_hyperedge([1, 5], start=0) + h.add_hyperedge([2, 5], start=0) + h.add_hyperedge([2, 6], start=0) + h.add_hyperedge([3, 6], start=0) + return h diff --git a/ash_model/test/generators/__init__.py b/ash_model/test/generators/__init__.py new file mode 100644 index 0000000..fe0a48e --- /dev/null +++ b/ash_model/test/generators/__init__.py @@ -0,0 +1 @@ +"""Tests for hypergraph generators.""" diff --git a/ash_model/test/generators/test_generators.py b/ash_model/test/generators/test_generators.py new file mode 100644 index 0000000..0942013 --- /dev/null +++ b/ash_model/test/generators/test_generators.py @@ -0,0 +1,172 @@ +import unittest +import random +import numpy as np + +from ash_model import ASH, NProfile +from ash_model.generators.random import random_hypergraph, random_ash +from ash_model.generators.homophily_driven import ( + _compute_probs_hba, + _random_hyperedge, + _truncated_pareto, + _sample_to_prob_distr, + ba_with_homophily, +) + + +class RandomGeneratorsTestCase(unittest.TestCase): + def setUp(self): + self.num_nodes = 10 + self.size_distr = {1: 3, 2: 4, 3: 2} + self.time_steps = 5 + self.node_attrs = {"color": ["red", "green", "blue"], "age": [20, 30, 40]} + self.seed = 42 + + def test_random_hypergraph_determinism(self): + h1 = random_hypergraph( + self.num_nodes, self.size_distr, self.node_attrs, seed=self.seed + ) + h2 = random_hypergraph( + self.num_nodes, self.size_distr, self.node_attrs, seed=self.seed + ) + self.assertEqual(set(h1.nodes()), set(h2.nodes())) + self.assertEqual(set(h1.hyperedges()), set(h2.hyperedges())) + for e in h1.hyperedges(): + self.assertEqual(h1.hyperedge_presence(e), h2.hyperedge_presence(e)) + for n in h1.nodes(): + self.assertEqual( + h1.get_node_attributes(n, tid=0), h2.get_node_attributes(n, tid=0) + ) + + def test_random_hypergraph_structure(self): + h = random_hypergraph( + self.num_nodes, self.size_distr, node_attrs=None, seed=self.seed + ) + self.assertEqual(set(h.nodes()), set(range(self.num_nodes))) + total_edges = sum(self.size_distr.values()) + self.assertEqual(h.number_of_hyperedges(start=0, end=0), total_edges) + sizes = [len(h.get_hyperedge_nodes(e)) for e in h.hyperedges(0, 0)] + for size, count in self.size_distr.items(): + self.assertEqual(sizes.count(size), count) + + def test_random_ash_determinism(self): + G1 = random_ash( + self.num_nodes, + self.size_distr, + self.time_steps, + self.node_attrs, + seed=self.seed, + ) + G2 = random_ash( + self.num_nodes, + self.size_distr, + self.time_steps, + self.node_attrs, + seed=self.seed, + ) + for n in range(self.num_nodes): + pres1 = G1.node_presence(n, as_intervals=False) + pres2 = G2.node_presence(n, as_intervals=False) + self.assertEqual(pres1, pres2) + for t in pres1: + self.assertEqual( + G1.get_node_attributes(n, tid=t), G2.get_node_attributes(n, tid=t) + ) + hes1 = sorted(G1.hyperedges()) + hes2 = sorted(G2.hyperedges()) + self.assertEqual(hes1, hes2) + for e in hes1: + self.assertEqual( + G1.hyperedge_presence(e, as_intervals=False), + G2.hyperedge_presence(e, as_intervals=False), + ) + + def test_random_ash_structure(self): + G = random_ash( + self.num_nodes, + self.size_distr, + self.time_steps, + node_attrs=None, + seed=self.seed, + ) + for n in range(self.num_nodes): + intervals = G.node_presence(n, as_intervals=True) + self.assertEqual(intervals, [(0, self.time_steps - 1)]) + for e in G.hyperedges(): + intervals = G.hyperedge_presence(e, as_intervals=True) + self.assertEqual(intervals, [(0, self.time_steps - 1)]) + for t in range(self.time_steps): + self.assertEqual( + G.number_of_hyperedges(start=t, end=t), sum(self.size_distr.values()) + ) + distr = G.hyperedge_size_distribution(start=0, end=0) + self.assertEqual(distr, self.size_distr) + + +class HomophilyDrivenGeneratorsTestCase(unittest.TestCase): + def test_truncated_pareto_errors(self): + with self.assertRaises(ValueError): + _truncated_pareto(alpha=1.0, size=5, xmin=0, xmax=10) + with self.assertRaises(ValueError): + _truncated_pareto(alpha=1.0, size=5, xmin=2, xmax=1) + with self.assertRaises(ValueError): + _truncated_pareto(alpha=0, size=5, xmin=2, xmax=10) + + def test_truncated_pareto_output(self): + size = 1000 + xmin, xmax, alpha = 2.0, 5.0, 1.5 + samples = _truncated_pareto( + alpha=alpha, size=size, xmin=xmin, xmax=xmax, rng=np.random.default_rng(0) + ) + self.assertEqual(len(samples), size) + self.assertTrue((samples >= xmin).all() and (samples <= xmax).all()) + + def test_sample_to_prob_distr(self): + # zero-sum sample => uniform + uniform = _sample_to_prob_distr([0, 0, 0]) + self.assertEqual(uniform, [1 / 3, 1 / 3, 1 / 3]) + # normal sample + sample = [2, 3, 5] + probs = _sample_to_prob_distr(sample) + self.assertAlmostEqual(sum(probs), 1.0) + self.assertEqual(probs, [2 / 10, 3 / 10, 5 / 10]) + + def test_compute_probs_hba(self): + # build small ASH with 2 existing nodes and 1 new node + h = ASH() + # node 0: red, node 1: blue + h.add_node(0, start=0, end=0, attr_dict=NProfile(node_id=0, color="red")) + h.add_node(1, start=0, end=0, attr_dict=NProfile(node_id=1, color="blue")) + # new node 2: red + h.add_node(2, start=0, end=0, attr_dict=NProfile(node_id=2, color="red")) + hr = 0.8 + probs = _compute_probs_hba(h, node=2, homophily_rate=hr) + # should get [hr, 1-hr] + self.assertEqual(len(probs), 2) + self.assertAlmostEqual(probs[0], hr, places=6) + self.assertAlmostEqual(probs[1], 1 - hr, places=6) + + def test_ba_with_homophily_errors(self): + with self.assertRaises(ValueError): + ba_with_homophily(5, m=1, homophily_rate=-0.1, minority_size=0.5, n0=1) + with self.assertRaises(ValueError): + ba_with_homophily(5, m=1, homophily_rate=0.5, minority_size=1.5, n0=1) + + def test_ba_with_homophily_basic(self): + random.seed(0) + np.random.seed(0) + num_nodes, m, hr, ms, n0 = 4, 1, 0.5, 0.5, 1 + # fixed two-size distribution for determinism + size_prob_distr = [0.5, 0.5] + h = ba_with_homophily(num_nodes, m, hr, ms, n0, size_prob_distr=size_prob_distr) + self.assertIsInstance(h, ASH) + # every node got a color attribute + for n in range(num_nodes): + c = h.get_node_attribute(n, "color", tid=0) + self.assertIn(c, {"red", "blue"}) + # coverage and uniformity should be 1.0 (all present at t=0) + self.assertEqual(h.coverage(), 1.0) + self.assertEqual(h.uniformity(), 1.0) + # each hyperedge size between 2 and 1+len(size_prob_distr) + for e in h.hyperedges(start=0, end=0): + sz = len(h.get_hyperedge_nodes(e)) + self.assertIn(sz, {2, 3}) diff --git a/ash_model/test/integration/__init__.py b/ash_model/test/integration/__init__.py new file mode 100644 index 0000000..d8da4f1 --- /dev/null +++ b/ash_model/test/integration/__init__.py @@ -0,0 +1 @@ +"""Integration tests for complete workflows.""" diff --git a/ash_model/test/integration/test_backends.py b/ash_model/test/integration/test_backends.py new file mode 100644 index 0000000..c096870 --- /dev/null +++ b/ash_model/test/integration/test_backends.py @@ -0,0 +1,233 @@ +"""Integration tests comparing Dense and Interval backends.""" + +import unittest +import numpy as np + +from ash_model import ASH + + +class BackendIntegrationTestCase(unittest.TestCase): + """Test that Dense and Interval backends produce identical results.""" + + def test_identical_node_operations(self): + """Test that both backends handle node operations identically.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Add same nodes to both + for i in range(1, 6): + h_dense.add_node(i, start=0, end=10) + h_interval.add_node(i, start=0, end=10) + + # Verify same nodes present + self.assertEqual(set(h_dense.nodes()), set(h_interval.nodes())) + self.assertEqual(h_dense.number_of_nodes(), h_interval.number_of_nodes()) + + def test_identical_hyperedge_operations(self): + """Test that both backends handle hyperedge operations identically.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Add same hyperedges + edges = [[1, 2, 3], [2, 3, 4], [3, 4, 5]] + for edge in edges: + h_dense.add_hyperedge(edge, start=0, end=5) + h_interval.add_hyperedge(edge, start=0, end=5) + + # Verify same hyperedges + self.assertEqual(set(h_dense.hyperedges()), set(h_interval.hyperedges())) + self.assertEqual( + h_dense.number_of_hyperedges(), h_interval.number_of_hyperedges() + ) + + def test_identical_temporal_queries(self): + """Test that temporal queries return same results.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Add temporal data + h_dense.add_hyperedge([1, 2], start=0, end=2) + h_dense.add_hyperedge([2, 3], start=1, end=3) + h_dense.add_hyperedge([1, 3], start=2, end=4) + + h_interval.add_hyperedge([1, 2], start=0, end=2) + h_interval.add_hyperedge([2, 3], start=1, end=3) + h_interval.add_hyperedge([1, 3], start=2, end=4) + + # Check temporal snapshots + self.assertEqual( + h_dense.temporal_snapshots_ids(), h_interval.temporal_snapshots_ids() + ) + + # Check node presence + for t in range(5): + self.assertEqual( + set(h_dense.nodes(start=t, end=t)), + set(h_interval.nodes(start=t, end=t)), + ) + + def test_identical_node_presence(self): + """Test that node_presence returns identical results.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Add node with complex temporal pattern + h_dense.add_node(1, start=0, end=2) + h_dense.add_node(1, start=5, end=7) + h_dense.add_node(1, start=10, end=12) + + h_interval.add_node(1, start=0, end=2) + h_interval.add_node(1, start=5, end=7) + h_interval.add_node(1, start=10, end=12) + + # Check presence as times + self.assertEqual(h_dense.node_presence(1), h_interval.node_presence(1)) + + # Check presence as intervals + self.assertEqual( + h_dense.node_presence(1, as_intervals=True), + h_interval.node_presence(1, as_intervals=True), + ) + + def test_identical_hyperedge_presence(self): + """Test that hyperedge_presence returns identical results.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Add hyperedge with gaps + h_dense.add_hyperedge([1, 2, 3], start=0, end=2) + h_dense.add_hyperedge([1, 2, 3], start=5, end=7) + + h_interval.add_hyperedge([1, 2, 3], start=0, end=2) + h_interval.add_hyperedge([1, 2, 3], start=5, end=7) + + # Get hyperedge id + eid_dense = h_dense.get_hyperedge_id([1, 2, 3]) + eid_interval = h_interval.get_hyperedge_id([1, 2, 3]) + + # Check presence + self.assertEqual( + h_dense.hyperedge_presence(eid_dense), + h_interval.hyperedge_presence(eid_interval), + ) + + self.assertEqual( + h_dense.hyperedge_presence(eid_dense, as_intervals=True), + h_interval.hyperedge_presence(eid_interval, as_intervals=True), + ) + + def test_identical_degree_calculations(self): + """Test that degree calculations are identical.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Build same hypergraph + edges = [[1, 2], [2, 3], [1, 2, 3], [3, 4]] + for edge in edges: + h_dense.add_hyperedge(edge, start=0) + h_interval.add_hyperedge(edge, start=0) + + # Check degrees for all nodes + for node in [1, 2, 3, 4]: + self.assertEqual( + h_dense.degree(node, start=0), h_interval.degree(node, start=0) + ) + + def test_identical_star_operations(self): + """Test that star() returns identical results.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + edges = [[1, 2, 3], [1, 4], [2, 3, 4]] + for edge in edges: + h_dense.add_hyperedge(edge, start=0) + h_interval.add_hyperedge(edge, start=0) + + # Check star for each node + for node in [1, 2, 3, 4]: + self.assertEqual( + set(h_dense.star(node, start=0)), set(h_interval.star(node, start=0)) + ) + + def test_identical_stream_interactions(self): + """Test that stream_interactions produces same events.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Add temporal hyperedges + h_dense.add_hyperedge([1, 2], start=0, end=2) + h_dense.add_hyperedge([2, 3], start=1, end=3) + + h_interval.add_hyperedge([1, 2], start=0, end=2) + h_interval.add_hyperedge([2, 3], start=1, end=3) + + # Collect streams + stream_dense = list(h_dense.stream_interactions()) + stream_interval = list(h_interval.stream_interactions()) + + # Should have same events + self.assertEqual(len(stream_dense), len(stream_interval)) + self.assertEqual(set(stream_dense), set(stream_interval)) + + def test_identical_with_attributes(self): + """Test that backends handle attributes identically.""" + h_dense = ASH(backend="dense") + h_interval = ASH(backend="interval") + + # Add nodes with attributes + attrs = {"name": "Alice", "age": 30} + h_dense.add_node(1, start=0, end=2, attr_dict=attrs) + h_interval.add_node(1, start=0, end=2, attr_dict=attrs) + + # Check attributes + self.assertEqual( + h_dense.get_node_attributes(1), h_interval.get_node_attributes(1) + ) + + # Add hyperedge with attributes + hedge_attrs = {"weight": 2.5, "type": "collab"} + h_dense.add_hyperedge([1, 2], start=0, **hedge_attrs) + h_interval.add_hyperedge([1, 2], start=0, **hedge_attrs) + + eid_dense = h_dense.get_hyperedge_id([1, 2]) + eid_interval = h_interval.get_hyperedge_id([1, 2]) + + self.assertEqual( + h_dense.get_hyperedge_attributes(eid_dense), + h_interval.get_hyperedge_attributes(eid_interval), + ) + + def test_performance_characteristics(self): + """Test that backends have expected performance characteristics for different patterns.""" + import time + + # Dense pattern: many short-lived entities + h_dense_backend = ASH(backend="dense") + h_interval_backend = ASH(backend="interval") + + # Add many short-lived hyperedges + n_edges = 100 + + start_dense = time.time() + for i in range(n_edges): + h_dense_backend.add_hyperedge([i, i + 1], start=i, end=i) + time_dense = time.time() - start_dense + + start_interval = time.time() + for i in range(n_edges): + h_interval_backend.add_hyperedge([i, i + 1], start=i, end=i) + time_interval = time.time() - start_interval + + # Both should complete reasonably fast (< 1 second) + self.assertLess(time_dense, 1.0) + self.assertLess(time_interval, 1.0) + + # Verify same result + self.assertEqual( + h_dense_backend.number_of_hyperedges(), + h_interval_backend.number_of_hyperedges(), + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/integration/test_workflows.py b/ash_model/test/integration/test_workflows.py new file mode 100644 index 0000000..a3f8db1 --- /dev/null +++ b/ash_model/test/integration/test_workflows.py @@ -0,0 +1,226 @@ +"""Integration tests for complete analysis workflows.""" + +import unittest +import numpy as np + +from ash_model import ASH, NProfile +from ash_model.measures import attribute_consistency, average_group_degree + + +class WorkflowIntegrationTestCase(unittest.TestCase): + """Test complete analysis workflows from data loading to results.""" + + def test_attribute_analysis_workflow(self): + """Test complete workflow for attribute homophily analysis.""" + # 1. Create hypergraph with attributed nodes + h = ASH() + + # Add nodes with group and numeric attributes + for i in range(1, 11): + group = "A" if i <= 5 else "B" + h.add_node(i, start=0, end=5, attr_dict={"group": group, "value": i * 10}) + + # 2. Add hyperedges with some homophilic structure + # Group A mostly connects within itself + h.add_hyperedge([1, 2, 3], start=0) + h.add_hyperedge([2, 3, 4], start=1) + h.add_hyperedge([4, 5], start=2) + + # Group B mostly connects within itself + h.add_hyperedge([6, 7, 8], start=0) + h.add_hyperedge([7, 8, 9], start=1) + h.add_hyperedge([9, 10], start=2) + + # Some cross-group connections + h.add_hyperedge([5, 6], start=3) + + # 3. Compute homophily measures + consistency = attribute_consistency(h, node=1) + avg_degree_data = average_group_degree(h, tid=0) + avg_degree_A = avg_degree_data["group"]["A"] + avg_degree_B = avg_degree_data["group"]["B"] + + # 4. Verify results make sense + self.assertIsInstance(consistency, dict) + self.assertGreater(avg_degree_A, 0) + self.assertGreater(avg_degree_B, 0) + + def test_temporal_evolution_workflow(self): + """Test workflow analyzing temporal evolution of hypergraph structure.""" + h = ASH() + + # Build evolving hypergraph + for t in range(10): + # Add new nodes over time + new_nodes = list(range(t * 3 + 1, (t + 1) * 3 + 1)) + for node in new_nodes: + h.add_node(node, start=t, end=t + 2) + + # Add hyperedges connecting recent nodes + if t > 0: + h.add_hyperedge(new_nodes, start=t) + + # Analyze temporal evolution + snapshots = h.temporal_snapshots_ids() + node_counts = [h.number_of_nodes(start=t, end=t) for t in snapshots] + edge_counts = [h.number_of_hyperedges(start=t, end=t) for t in snapshots] + + # Verify growth + self.assertGreater(len(snapshots), 0) + self.assertGreater(max(node_counts), min(node_counts)) + self.assertGreater(max(edge_counts), 0) + + # Check temporal metrics + coverage = h.coverage() + uniformity = h.uniformity() + + self.assertGreaterEqual(coverage, 0.0) + self.assertLessEqual(coverage, 1.0) + self.assertGreaterEqual(uniformity, 0.0) + self.assertLessEqual(uniformity, 1.0) + + def test_clustering_analysis_workflow(self): + """Test workflow for degree-based structural analysis.""" + h = ASH() + + # Create hypergraph with clustered structure + # Cluster 1 + h.add_hyperedge([1, 2, 3], start=0) + h.add_hyperedge([2, 3, 4], start=0) + h.add_hyperedge([1, 3, 4], start=0) + + # Cluster 2 + h.add_hyperedge([5, 6, 7], start=0) + h.add_hyperedge([6, 7, 8], start=0) + + # Bridge + h.add_hyperedge([4, 5], start=0) + + # Compute degree-based metrics + degree_results = {} + for node in h.nodes(start=0): + deg = h.degree(node, start=0) + degree_results[node] = deg + + # Verify all nodes have valid degrees + for node, deg in degree_results.items(): + self.assertIsNotNone(deg) + self.assertGreaterEqual(deg, 0) + + def test_projection_and_analysis_workflow(self): + """Test workflow using projections for analysis.""" + h = ASH() + + # Build bipartite-like structure + # Authors: 1, 2, 3, 4 + # Papers: represented as hyperedges + h.add_hyperedge([1, 2], start=0) # Paper 1 + h.add_hyperedge([2, 3], start=0) # Paper 2 + h.add_hyperedge([1, 2, 3], start=0) # Paper 3 + h.add_hyperedge([3, 4], start=0) # Paper 4 + + # Create clique projection (co-authorship network) + from ash_model.utils import clique_projection + + G = clique_projection(h, start=0) + + # Analyze projected graph + self.assertGreater(G.number_of_nodes(), 0) + self.assertGreater(G.number_of_edges(), 0) + + # Check edge weights (number of co-authorships) + for u, v, data in G.edges(data=True): + self.assertIn("weight", data) + self.assertGreater(data["weight"], 0) + + def test_profile_aggregation_workflow(self): + """Test workflow with node profile aggregation.""" + h = ASH() + + # Add node with evolving attributes + h.add_node(1, start=0, attr_dict=NProfile(node_id=1, value=10, category="A")) + h.add_node(1, start=1, attr_dict=NProfile(node_id=1, value=20, category="A")) + h.add_node(1, start=2, attr_dict=NProfile(node_id=1, value=30, category="B")) + h.add_node(1, start=3, attr_dict=NProfile(node_id=1, value=40, category="B")) + + # Get aggregated profile + agg_profile = h.get_node_profile(1) # No tid = aggregation + + # Check aggregation + self.assertIsNotNone(agg_profile) + attrs = agg_profile.get_attributes() + + # Numeric should be averaged + self.assertIn("value", attrs) + self.assertAlmostEqual(attrs["value"], 25.0, delta=1.0) + + # Categorical should be most frequent + self.assertIn("category", attrs) + # B appears twice, A appears twice, so could be either + self.assertIn(attrs["category"], ["A", "B"]) + + def test_io_roundtrip_workflow(self): + """Test complete workflow saving and loading hypergraph.""" + import tempfile + import os + from ash_model.readwrite import write_ash_to_json, read_ash_from_json + + # Create hypergraph + h_original = ASH() + h_original.add_node(1, start=0, end=2, attr_dict={"name": "Alice"}) + h_original.add_node(2, start=0, end=2, attr_dict={"name": "Bob"}) + h_original.add_hyperedge([1, 2], start=0, end=1, weight=2.5) + + # Save to temp file + with tempfile.NamedTemporaryFile(mode="w", suffix=".json", delete=False) as f: + temp_path = f.name + + try: + write_ash_to_json(h_original, temp_path) + + # Load back + h_loaded = read_ash_from_json(temp_path) + + # Verify preservation + self.assertEqual(set(h_original.nodes()), set(h_loaded.nodes())) + self.assertEqual(set(h_original.hyperedges()), set(h_loaded.hyperedges())) + self.assertEqual( + h_original.get_node_attributes(1), h_loaded.get_node_attributes(1) + ) + finally: + if os.path.exists(temp_path): + os.unlink(temp_path) + + def test_generator_and_analysis_workflow(self): + """Test workflow generating synthetic hypergraph and analyzing it.""" + from ash_model.generators import random_ash + + # Generate random hypergraph + h = random_ash( + num_nodes=20, + size_distr={2: 10, 3: 10, 4: 5, 5: 5}, # 30 total hyperedges + time_steps=5, + seed=42, + ) + + # Verify structure + self.assertEqual(h.number_of_nodes(), 20) + self.assertGreaterEqual(h.number_of_hyperedges(), 1) + + # Analyze degree distribution + degree_dist = h.degree_distribution() + self.assertIsInstance(degree_dist, dict) + self.assertGreater(len(degree_dist), 0) + + # Analyze size distribution + size_dist = h.hyperedge_size_distribution() + self.assertIsInstance(size_dist, dict) + self.assertGreater(len(size_dist), 0) + + # Check all sizes respect max_size constraint + for size in size_dist.keys(): + self.assertLessEqual(size, 5) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/io/__init__.py b/ash_model/test/io/__init__.py new file mode 100644 index 0000000..0d96a21 --- /dev/null +++ b/ash_model/test/io/__init__.py @@ -0,0 +1 @@ +"""Tests for I/O operations (reading/writing hypergraphs).""" diff --git 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new file mode 100644 index 0000000..5651f07 --- /dev/null +++ b/ash_model/test/io/hif_data/hif_schema.json @@ -0,0 +1,112 @@ +{ + "$schema": "http://json-schema.org/draft-07/schema#", + "$id": "https://raw.githubusercontent.com/pszufe/HIF_validators/main/schemas/schema.json", + "title": "Hypergraph Interchange Format", + "version": "latest", + "type": "object", + "properties": { + "network-type": { + "enum": [ + "undirected", + "directed", + "asc" + ] + }, + "metadata": { + "type": "object" + }, + "incidences": { + "type": "array", + "items": { + "type": "object", + "properties": { + "edge": { + "type": [ + "string", + "integer" + ] + }, + "node": { + "type": [ + "string", + "integer" + ] + }, + "weight": { + "type": "number" + }, + "direction": { + "enum": [ + "head", + "tail" + ] + }, + "attrs": { + "type": "object" + } + }, + "unevaluatedProperties": false, + "additionalProperties": false, + "required": [ + "edge", + "node" + ] + } + }, + "nodes": { + "type": "array", + "items": { + "type": "object", + "properties": { + "node": { + "type": [ + "string", + "integer" + ] + }, + "weight": { + "type": "number" + }, + "attrs": { + "type": "object" + } + }, + "unevaluatedProperties": false, + "additionalProperties": false, + "required": [ + "node" + ] + } + }, + "edges": { + "type": "array", + "items": { + "type": "object", + "properties": { + "edge": { + "type": [ + "string", + "integer" + ] + }, + "weight": { + "type": "number" + }, + "attrs": { + "type": "object" + } + }, + "unevaluatedProperties": false, + "additionalProperties": false, + "required": [ + "edge" + ] + } + } + }, + "unevaluatedProperties": false, + "additionalProperties": false, + "required": [ + "incidences" + ] +} \ No newline at end of file diff --git a/ash_model/test/io/test_io.py b/ash_model/test/io/test_io.py new file mode 100644 index 0000000..a5d642c --- /dev/null +++ b/ash_model/test/io/test_io.py @@ -0,0 +1,271 @@ +import os +import gzip +import json +import tempfile +import unittest + +import numpy as np + +from ash_model import ASH, NProfile +from ash_model.readwrite import ( + write_profiles_to_csv, + read_profiles_from_csv, + write_profiles_to_jsonl, + read_profiles_from_jsonl, + write_sh_to_csv, + read_sh_from_csv, + write_ash_to_json, + read_ash_from_json, + read_hif, + write_hif, +) + + +class IOTestCase(unittest.TestCase): + def setUp(self): + # a small hypergraph with node‐ and edge‐attributes and multi‐span edges + self.a = ASH() + # hyperedge e1 present at t=0..1, weight=3 + self.a.add_hyperedge([1, 2], start=0, end=1, weight=3) + # hyperedge e2 present only at t=2 + self.a.add_hyperedge([2, 3, 4], start=2, weight=5) + # nodes with profiles changing across time + self.a.add_node(1, start=0, end=1, attr_dict=NProfile(1, color="red", score=10)) + self.a.add_node( + 1, start=2, end=2, attr_dict=NProfile(1, color="blue", score=20) + ) + self.a.add_node( + 2, start=0, end=2, attr_dict=NProfile(2, color="green", score=5) + ) + + def _roundtrip_file(self, write_fn, read_fn, *args, **kwargs): + # helper: write to temp, read back, return result + tf = tempfile.NamedTemporaryFile(delete=False) + tf.close() + try: + write_fn(self.a, tf.name, *args, **kwargs) + return read_fn(tf.name, *args, **kwargs) + finally: + os.remove(tf.name) + + def test_profiles_csv_roundtrip_default(self): + # write and read back + res = self._roundtrip_file(write_profiles_to_csv, read_profiles_from_csv) + # Should have exactly nodes 1 and 2: + self.assertCountEqual(res.keys(), [1, 2, 3, 4]) + # Node 1: tids 0,1,2 + self.assertCountEqual(res[1].keys(), [0, 1, 2]) + # Check types: score remains int, color is str + p0 = res[1][0] + attrs = p0.get_attributes() + self.assertIsInstance(attrs["score"], int) + self.assertIsInstance(attrs["color"], str) + # Check actual values + self.assertEqual(attrs["color"], "red") + self.assertEqual(attrs["score"], 10) + + def test_profiles_csv_custom_delimiter_and_header(self): + # use semicolon + tf = tempfile.NamedTemporaryFile(delete=False) + tf.close() + try: + write_profiles_to_csv(self.a, tf.name, delimiter=";") + # check header line + with open(tf.name) as f: + header = f.readline().strip().split(";") + # must start with node_id, tid, then sorted attribute names + self.assertEqual(header[0:2], ["node_id", "tid"]) + self.assertEqual(set(header[2:]), {"color", "score"}) + # now roundtrip + res = read_profiles_from_csv(tf.name, delimiter=";") + self.assertCountEqual(res.keys(), [1, 2, 3, 4]) + finally: + os.remove(tf.name) + + def test_profiles_csv_empty_graph(self): + empty = ASH() + tf = tempfile.NamedTemporaryFile(delete=False) + tf.close() + try: + write_profiles_to_csv(empty, tf.name) + # file should either not exist or only header + lines = open(tf.name).read().splitlines() + # no header written (no nodes) + self.assertTrue(len(lines) in (0, 1)) + finally: + os.remove(tf.name) + + def test_profiles_jsonl_roundtrip(self): + # uncompressed + res = self._roundtrip_file( + write_profiles_to_jsonl, read_profiles_from_jsonl, compress=False + ) + self.assertCountEqual(res.keys(), [1, 2, 3, 4]) + # compressed + res2 = self._roundtrip_file( + write_profiles_to_jsonl, read_profiles_from_jsonl, compress=True + ) + self.assertCountEqual(res2.keys(), [1, 2, 3, 4]) + + def test_sh_csv_roundtrip_and_header(self): + # write hyperedges + tf = tempfile.NamedTemporaryFile(delete=False) + tf.close() + try: + write_sh_to_csv(self.a, tf.name) + # header must be present + with open(tf.name) as f: + hdr = f.readline().strip() + self.assertEqual(hdr, "nodes\tstart,end") + # roundtrip + b = read_sh_from_csv(tf.name) + # same hyperedges + sets_a = [ + frozenset(self.a.get_hyperedge_nodes(h)) for h in self.a.hyperedges() + ] + sets_b = [frozenset(b.get_hyperedge_nodes(h)) for h in b.hyperedges()] + + self.assertCountEqual(sets_b, sets_a) + # presence times match + sets_a = [ + frozenset(self.a.hyperedge_presence(h)) for h in self.a.hyperedges() + ] + sets_b = [frozenset(b.hyperedge_presence(h)) for h in b.hyperedges()] + self.assertCountEqual(sets_b, sets_a) + + finally: + os.remove(tf.name) + + def test_ash_json_roundtrip_uncompressed_and_compressed(self): + # uncompressed + for compress in (False, True): + # write + tf = tempfile.NamedTemporaryFile(delete=False) + tf.close() + try: + write_ash_to_json(self.a, tf.name, compress=compress) + b = read_ash_from_json(tf.name, compress=compress) + # same nodes + self.assertCountEqual(b.nodes(), self.a.nodes()) + # same hyperedges + self.assertCountEqual(b.hyperedges(), self.a.hyperedges()) + # same snapshots + self.assertEqual( + sorted(b.temporal_snapshots_ids()), + sorted(self.a.temporal_snapshots_ids()), + ) + # edge attributes (weight) preserved + weights_a = [ + self.a.get_hyperedge_weight(h) for h in self.a.hyperedges() + ] + weights_b = [b.get_hyperedge_weight(h) for h in b.hyperedges()] + self.assertCountEqual(weights_a, weights_b) + + # node profiles equal + for n in self.a.nodes(): + for t in self.a.node_presence(n): + p1 = self.a.get_node_profile(n, t) + p2 = b.get_node_profile(n, t) + self.assertEqual(p1, p2) + finally: + os.remove(tf.name) + + def test_read_write_missing_file_raises(self): + # read functions should raise if file not found + with self.assertRaises(FileNotFoundError): + read_profiles_from_csv("no_such_file.csv") + with self.assertRaises(FileNotFoundError): + read_profiles_from_jsonl("no_such_file.jsonl") + with self.assertRaises(FileNotFoundError): + read_sh_from_csv("no_such_file.csv") + with self.assertRaises(FileNotFoundError): + read_ash_from_json("no_such_file.json") + + def test_hif_ash(self): + import fastjsonschema + import json + + base = os.path.join(os.path.dirname(__file__), "hif_data") + schema_path = os.path.join(base, "hif_schema.json") + with open(schema_path) as f: + schema = json.load(f) + validator = fastjsonschema.compile(schema) + + # write + tf = tempfile.NamedTemporaryFile(delete=False) + tf.close() + + write_hif(self.a, tf.name) + + with open(tf.name) as tmp: + data = json.loads(tmp.read()) + + try: + validator(data) + except Exception: + raise ValueError("invalid hif") + + a2 = read_hif(tf.name) + + # check equivalence + try: + # same nodes + self.assertCountEqual(a2.nodes(), self.a.nodes()) + + # same hyperedges (by node sets, since edge IDs may differ) + sets_a = [ + frozenset(self.a.get_hyperedge_nodes(h)) for h in self.a.hyperedges() + ] + sets_a2 = [frozenset(a2.get_hyperedge_nodes(h)) for h in a2.hyperedges()] + self.assertCountEqual(sets_a2, sets_a) + + # same temporal snapshots + self.assertEqual( + sorted(a2.temporal_snapshots_ids()), + sorted(self.a.temporal_snapshots_ids()), + ) + + # check hyperedge presence times match for corresponding edges + for h1 in self.a.hyperedges(): + nodes1 = frozenset(self.a.get_hyperedge_nodes(h1)) + presence1 = frozenset(self.a.hyperedge_presence(h1)) + + # find corresponding edge in a2 + found = False + for h2 in a2.hyperedges(): + nodes2 = frozenset(a2.get_hyperedge_nodes(h2)) + if nodes1 == nodes2: + presence2 = frozenset(a2.hyperedge_presence(h2)) + if presence1 == presence2: + # check edge attributes match + weight1 = self.a.get_hyperedge_weight(h1) + weight2 = a2.get_hyperedge_weight(h2) + self.assertEqual(weight1, weight2) + found = True + break + + self.assertTrue(found, f"Could not find matching edge for {nodes1}") + + # check node profiles are preserved + for n in self.a.nodes(): + for t in self.a.node_presence(n): + if n in a2.nodes() and t in a2.node_presence(n): + p1 = self.a.get_node_profile(n, t) + p2 = a2.get_node_profile(n, t) + self.assertEqual(p1, p2) + + finally: + os.remove(tf.name) + + def test_hif_static(self): + base = os.path.join(os.path.dirname(__file__), "hif_data") + data_path = os.path.join(base, "email-enron.hif") + h = read_hif(data_path) + self.assertIsInstance(h, ASH) + self.assertListEqual(h.temporal_snapshots_ids(), [0]) + self.assertGreaterEqual(h.number_of_nodes(), 143) + self.assertGreaterEqual(h.number_of_hyperedges(), 1436) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/measures/__init__.py b/ash_model/test/measures/__init__.py new file mode 100644 index 0000000..c0bd5f5 --- /dev/null +++ b/ash_model/test/measures/__init__.py @@ -0,0 +1 @@ +"""Tests for hypergraph measures and metrics.""" diff --git a/ash_model/test/measures/test_attribute_analysis.py b/ash_model/test/measures/test_attribute_analysis.py new file mode 100644 index 0000000..56d3266 --- /dev/null +++ b/ash_model/test/measures/test_attribute_analysis.py @@ -0,0 +1,195 @@ +import unittest +import math +import numpy as np + +from ash_model.measures.attribute_analysis import ( + hyperedge_profile_purity, + hyperedge_profile_entropy, + star_profile_entropy, + star_profile_homogeneity, + average_group_degree, + attribute_consistency, +) +from ash_model.measures import ASH, NProfile + + +class AttributeAnalysisCase(unittest.TestCase): + @staticmethod + def get_hypergraph(): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([1, 2, 3, 4], 0) + a.add_hyperedge([1, 3, 4], 1) + a.add_hyperedge([3, 4], 1) + + a.add_node( + 1, + start=0, + end=0, + attr_dict=NProfile(node_id=1, party="L", age=37, gender="M"), + ) + a.add_node( + 1, + start=1, + end=1, + attr_dict=NProfile(node_id=1, party="R", age=37, gender="M"), + ) + a.add_node( + 2, + start=0, + end=0, + attr_dict=NProfile(node_id=2, party="L", age=20, gender="F"), + ) + a.add_node( + 3, + start=0, + end=1, + attr_dict=NProfile(node_id=3, party="L", age=11, gender="F"), + ) + a.add_node( + 4, + start=0, + end=1, + attr_dict=NProfile(node_id=4, party="R", age=45, gender="M"), + ) + return a + + def test_hyperedge_profile_purity(self): + a = self.get_hypergraph() + # find the hyperedge [3,4] at tid=1 + hes = list(a.hyperedges(start=1)) + he = next(h for h in hes if set(a.get_hyperedge_nodes(h)) == {3, 4}) + + purity = hyperedge_profile_purity(a, he, 1) + # for party, labels ['L','R'] => most common 'L' + # for gender, labels ['F','M'] => most common 'F' + self.assertEqual(purity["party"], {"L": 0.5}) + self.assertEqual(purity["gender"], {"F": 0.5}) + + # keys should be exactly these two + self.assertListEqual(sorted(purity.keys()), ["gender", "party"]) + + def test_hyperedge_profile_purity_single_class_and_entropy_zero(self): + a = self.get_hypergraph() + # at tid=0 the hyperedge [1,2,3] has party all 'L' + he = next( + h + for h in a.hyperedges(start=0) + if set(a.get_hyperedge_nodes(h)) == {1, 2, 3} + ) + purity = hyperedge_profile_purity(a, he, 0) + self.assertEqual(purity["party"], {"L": 1.0}) + # gender has two 'F' and one 'M' => purity 2/3 + self.assertEqual(purity["gender"], {"F": 2 / 3}) + + ent = hyperedge_profile_entropy(a, he, tid=0) + # single class => entropy 0 + self.assertAlmostEqual(ent["party"], 0.0) + # gender has 2 classes + self.assertGreater(ent["gender"], 0.0) + + def test_hyperedge_profile_entropy(self): + a = self.get_hypergraph() + hes = list(a.hyperedges(start=1)) + he = next(h for h in hes if set(a.get_hyperedge_nodes(h)) == {3, 4}) + + ent = hyperedge_profile_entropy(a, he, tid=1) + # for ['L','R'] with base=2 ⇒ entropy=1.0 + self.assertAlmostEqual(ent["party"], 1.0) + self.assertAlmostEqual(ent["gender"], 1.0) + + self.assertListEqual(sorted(ent.keys()), ["gender", "party"]) + + def test_star_profile_entropy(self): + a = self.get_hypergraph() + # collapse method at tid=0, node=1: star nodes {1,2,3,4} + res = star_profile_entropy(a, node_id=1, tid=0, method="collapse") + # party labels ['L','L','L','R'] + p = -(2 / 3 * math.log(2 / 3, 2) + 1 / 3 * math.log(1 / 3, 2)) + self.assertAlmostEqual(res["party"], p, places=6) + # gender labels ['M','F','F','M'] + + self.assertAlmostEqual(res["gender"], 0.918, places=3) + + def test_star_profile_entropy_aggregate_and_invalid(self): + a = self.get_hypergraph() + # aggregate method path + res = star_profile_entropy(a, node_id=1, tid=0, method="aggregate") + # still returns dict with categorical attrs + self.assertIn("party", res) + self.assertIn("gender", res) + # invalid method raises + with self.assertRaises(ValueError): + star_profile_entropy(a, node_id=1, tid=0, method="unknown") + + def test_star_profile_homogeneity(self): + a = self.get_hypergraph() + # collapse method at tid=0, node=1: 3 hyperedges. attributes: gender(1)='M', party(1)='L' + res = star_profile_homogeneity(a, node_id=1, tid=0, method="collapse") + # party: 2 of the 3 neighbors have the same party 'L', 1 has 'R' ⇒ homogeneity=2/3 + self.assertAlmostEqual(res["party"], 2 / 3) + # gender: 1 of the 3 neighbors have the same gender 'M', 2 has 'F' ⇒ homogeneity= 1/3 + self.assertAlmostEqual(res["gender"], 1 / 3) + + def test_star_profile_homogeneity_aggregate_and_invalid(self): + a = self.get_hypergraph() + res = star_profile_homogeneity(a, node_id=1, tid=0, method="aggregate") + self.assertIn("party", res) + self.assertIn("gender", res) + with self.assertRaises(ValueError): + star_profile_homogeneity(a, node_id=1, tid=0, method="bad") + + def test_average_group_degree(self): + a = self.get_hypergraph() + out = average_group_degree(a, tid=0) + # at tid=0, degrees are: + # party L: nodes 1,2,3 have degrees 3,2,2 ⇒ mean 7/3 + # party R: node 4 has degree 2 ⇒ mean 2 + self.assertAlmostEqual(out["party"]["L"], 7 / 3) + self.assertAlmostEqual(out["party"]["R"], 2.0) + # gender M: nodes 1,4 => 3,2 ⇒ 2.5 + # gender F: nodes 2,3 => 2,2 ⇒ 2.0 + self.assertAlmostEqual(out["gender"]["M"], 2.5) + self.assertAlmostEqual(out["gender"]["F"], 2.0) + + def test_average_group_degree_hyperedge_size_filter(self): + a = self.get_hypergraph() + # consider only hyperedges of size exactly 3 at tid=0 + out = average_group_degree(a, tid=0, hyperedge_size=3) + self.assertAlmostEqual(out["party"]["L"], 1.0) # nodes 1,2,3 each deg=1 + self.assertAlmostEqual(out["party"]["R"], 0.0) # node 4 has deg=0 + + def test_attribute_consistency(self): + a = self.get_hypergraph() + cons = attribute_consistency(a) + # Node 1: party changed L→R ⇒ consistency=0; gender stayed M⇒1 + self.assertAlmostEqual(cons[1]["party"], 0.0) + self.assertAlmostEqual(cons[1]["gender"], 1.0) + # Node 2 only at tid=0 ⇒ consistency=1 for both + self.assertAlmostEqual(cons[2]["party"], 1.0) + self.assertAlmostEqual(cons[2]["gender"], 1.0) + # Node 3 (L→L, F→F) ⇒ both 1 + self.assertAlmostEqual(cons[3]["party"], 1.0) + self.assertAlmostEqual(cons[3]["gender"], 1.0) + # Node 4 (R→R, M→M) ⇒ both 1 + self.assertAlmostEqual(cons[4]["party"], 1.0) + self.assertAlmostEqual(cons[4]["gender"], 1.0) + + def test_attribute_consistency_node_param_and_zero(self): + a = self.get_hypergraph() + # add node 0 with stable attributes across times + a.add_node( + 0, start=0, end=1, attr_dict=NProfile(node_id=0, party="X", gender="M") + ) + only0 = attribute_consistency(a, node=0) + self.assertSetEqual(set(only0.keys()), {"party", "gender"}) + self.assertAlmostEqual(only0["party"], 1.0) + self.assertAlmostEqual(only0["gender"], 1.0) + # specifying node limits output to that node + only1 = attribute_consistency(a, node=1) + self.assertSetEqual(set(only1.keys()), {"party", "gender"}) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/measures/test_centralities.py b/ash_model/test/measures/test_centralities.py new file mode 100644 index 0000000..f5caa66 --- /dev/null +++ b/ash_model/test/measures/test_centralities.py @@ -0,0 +1,135 @@ +import unittest + +from ash_model import ASH +from ash_model.measures import ( + s_betweenness_centrality, + s_closeness_centrality, + s_eccentricity, + s_eigenvector_centrality, + s_harmonic_centrality, + s_information_centrality, + s_katz, + s_load_centrality, + s_second_order_centrality, +) + + +class SCentralitiesCase(unittest.TestCase): + @staticmethod + def get_hypergraph(): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([1, 2, 3, 4], 0) + a.add_hyperedge([1, 3, 4], 1) + a.add_hyperedge([3, 4], 1) + return a + + def test_centralities(self): + a = self.get_hypergraph() + + # Betweenness centrality + self.assertDictEqual( + s_betweenness_centrality(a, s=1), + {"e1": 0.0, "e2": 0.0, "e3": 0.0, "e4": 0.0, "e5": 0.0}, + ) + self.assertDictEqual( + s_betweenness_centrality(a, s=1, edges=False), + {1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}, + ) + + # Closeness centrality + self.assertDictEqual( + s_closeness_centrality(a, s=1), + {"e1": 1.0, "e2": 1.0, "e3": 1.0, "e4": 1.0, "e5": 1.0}, + ) + self.assertDictEqual( + s_closeness_centrality(a, s=1, edges=False), + {1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0}, + ) + + # Eccentricity + self.assertDictEqual( + s_eccentricity(a, s=1), + {"e1": 1.0, "e2": 1.0, "e3": 1.0, "e4": 1.0, "e5": 1.0}, + ) + self.assertDictEqual( + s_eccentricity(a, s=1, edges=False), + {1: 1, 2: 1, 3: 1, 4: 1}, + ) + + # Harmonic centrality + self.assertDictEqual( + s_harmonic_centrality(a, s=1), + {"e1": 4.0, "e2": 4.0, "e3": 4.0, "e4": 4.0, "e5": 4.0}, + ) + self.assertDictEqual( + s_harmonic_centrality(a, s=1, edges=False), + {1: 3.0, 2: 3.0, 3: 3.0, 4: 3.0}, + ) + + # Katz centrality rounded to 3 decimals + katz_edge = s_katz(a, s=1) + katz_edge = {k: round(v, 3) for k, v in katz_edge.items()} + self.assertDictEqual( + katz_edge, + {"e1": 0.447, "e2": 0.447, "e3": 0.447, "e4": 0.447, "e5": 0.447}, + ) + katz_node = s_katz(a, s=1, edges=False) + katz_node = {k: round(v, 3) for k, v in katz_node.items()} + self.assertDictEqual( + katz_node, + {1: 0.5, 2: 0.5, 3: 0.5, 4: 0.5}, + ) + + # Load centrality + self.assertDictEqual( + s_load_centrality(a, s=1), + {"e1": 0.0, "e2": 0.0, "e3": 0.0, "e4": 0.0, "e5": 0.0}, + ) + self.assertDictEqual( + s_load_centrality(a, s=1, edges=False), + {1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}, + ) + + # Eigenvector centrality rounded to 3 decimals + eig_edge = s_eigenvector_centrality(a, s=1) + eig_edge = {k: round(v, 3) for k, v in eig_edge.items()} + self.assertDictEqual( + eig_edge, + {"e1": 0.447, "e2": 0.447, "e3": 0.447, "e4": 0.447, "e5": 0.447}, + ) + eig_node = s_eigenvector_centrality(a, s=1, edges=False) + eig_node = {k: round(v, 3) for k, v in eig_node.items()} + self.assertDictEqual( + eig_node, + {1: 0.5, 2: 0.5, 3: 0.5, 4: 0.5}, + ) + + # Information centrality rounded to 3 decimals + info_edge = s_information_centrality(a, s=1) + info_edge = {k: round(v, 3) for k, v in info_edge.items()} + self.assertDictEqual( + info_edge, + {"e1": 0.625, "e2": 0.625, "e3": 0.625, "e4": 0.625, "e5": 0.625}, + ) + info_node = s_information_centrality(a, s=1, edges=False) + info_node = {k: round(v, 3) for k, v in info_node.items()} + self.assertDictEqual( + info_node, + {1: 0.667, 2: 0.667, 3: 0.667, 4: 0.667}, + ) + + # Second-order centrality rounded to 3 decimals + sec_edge = s_second_order_centrality(a, s=1) + sec_edge = {k: round(v, 3) for k, v in sec_edge.items()} + self.assertDictEqual( + sec_edge, + {"e1": 3.464, "e2": 3.464, "e3": 3.464, "e4": 3.464, "e5": 3.464}, + ) + sec_node = s_second_order_centrality(a, s=1, edges=False) + sec_node = {k: round(v, 3) for k, v in sec_node.items()} + self.assertDictEqual( + sec_node, + {1: 2.449, 2: 2.449, 3: 2.449, 4: 2.449}, + ) diff --git a/ash_model/test/measures/test_clustering.py b/ash_model/test/measures/test_clustering.py new file mode 100644 index 0000000..a9e4448 --- /dev/null +++ b/ash_model/test/measures/test_clustering.py @@ -0,0 +1,103 @@ +import unittest + +from ash_model import ASH +from ash_model.measures import ( + average_s_local_clustering_coefficient, + inclusiveness, + s_intersections, + s_local_clustering_coefficient, +) + + +class ClusteringTestCase(unittest.TestCase): + def test_LCC(self): + a = ASH() + a.add_hyperedge([1, 2], 0) + a.add_hyperedge([1, 3], 0) + a.add_hyperedge([1, 4], 0) + + LCC = s_local_clustering_coefficient(a, 1, "e1") + self.assertEqual(LCC, 1) + + a = ASH() + a.add_hyperedge([1, 2, 3, 5], 0) + a.add_hyperedge([1, 2, 3, 4], 0) + a.add_hyperedge([1, 2, 3, 4, 5], 0) + + LCC = s_local_clustering_coefficient(a, 1, "e1") + self.assertEqual(LCC, 1) + + a = ASH() + a.add_hyperedge([1, 2, 6, 7], 0) + a.add_hyperedge([1, 2, 3, 4, 5], 0) + a.add_hyperedge([3, 4, 5, 6, 7], 0) + + LCC = s_local_clustering_coefficient(a, 1, "e1") + self.assertEqual(LCC, 1) + + a = ASH() + a.add_hyperedge([1, 2], 0) # “e1” + a.add_hyperedge([1, 3], 0) # “e2” + a.add_hyperedge([1, 4], 0) # “e3” + a.add_hyperedge([2, 5], 0) # “e4” + + lcc = s_local_clustering_coefficient(a, 1, "e1") + self.assertAlmostEqual(lcc, 1 / 3, places=6) + + def test_avg_LCC(self): + a = ASH() + a.add_hyperedge([1, 2], 0) + a.add_hyperedge([1, 3], 0) + a.add_hyperedge([1, 4], 0) + + LCC = average_s_local_clustering_coefficient(a, 1) + self.assertEqual(LCC, 1) + + a = ASH() + a.add_hyperedge([1, 2, 3, 5], 0) + a.add_hyperedge([1, 2, 3, 4], 0) + a.add_hyperedge([1, 2, 3, 4, 5], 0) + + LCC = average_s_local_clustering_coefficient(a, 1) + self.assertEqual(LCC, 1) + + a = ASH() + a.add_hyperedge([1, 2, 6, 7], 0) + a.add_hyperedge([1, 2, 3, 4, 5], 0) + a.add_hyperedge([3, 4, 5, 6, 7], 0) + + LCC = average_s_local_clustering_coefficient(a, 1) + self.assertEqual(LCC, 1) # TODO: CHECK THIS + + def test_s_intersections_and_inclusiveness(self): + a = ASH() + # Build at t=0 three hyperedges with overlaps: + # e1={1,2,3}, e2={2,3,4}, e3={1,2} + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([2, 3, 4], 0) + a.add_hyperedge([1, 2], 0) + # s=2: intersections are between e1-e2 (overlap {2,3}) and e1-e3 (overlap {1,2}) + inter = s_intersections(a, s=2, start=0, end=0) + self.assertEqual(inter, 2) + # inclusiveness: e3={1,2} is subset of e1 -> non-facet count=1 over total 3 => 1/3 + incl = inclusiveness(a, start=0, end=0) + self.assertAlmostEqual(incl, 1 / 3) + + def test_lcc_missing_hyperedge_and_small_k(self): + a = ASH() + # two hyperedges overlapping ⇒ line‑graph has 2 nodes (each degree 1) + a.add_hyperedge([1, 2], 0) # e1 + a.add_hyperedge([2, 3], 0) # e2 + # hyperedge not in line graph + self.assertEqual(s_local_clustering_coefficient(a, 1, "ex"), 0.0) + # k<2 ⇒ 0 + self.assertEqual(s_local_clustering_coefficient(a, 1, "e1"), 0.0) + + def test_avg_lcc_empty_graph_zero_and_inclusiveness_empty(self): + a = ASH() + # no hyperedges at this time window ⇒ empty line graph + self.assertEqual( + average_s_local_clustering_coefficient(a, 1, start=5, end=5), 0.0 + ) + # inclusiveness with no hyperedges ⇒ 0 + self.assertEqual(inclusiveness(a, start=5, end=5), 0.0) diff --git a/ash_model/test/test_hyperconformity.py b/ash_model/test/measures/test_hyperconformity.py similarity index 97% rename from ash_model/test/test_hyperconformity.py rename to ash_model/test/measures/test_hyperconformity.py index 3dfadc8..4b2f824 100644 --- a/ash_model/test/test_hyperconformity.py +++ b/ash_model/test/measures/test_hyperconformity.py @@ -1,8 +1,10 @@ -import unittest -from ash_model import ASH, NProfile -from ash_model.measures import * import json import os +import unittest +import numpy as np + +from ash_model import ASH, NProfile +from ash_model.measures import hyper_conformity class HyperConformityTestCase(unittest.TestCase): diff --git a/ash_model/test/measures/test_segregation.py b/ash_model/test/measures/test_segregation.py new file mode 100644 index 0000000..4179f26 --- /dev/null +++ b/ash_model/test/measures/test_segregation.py @@ -0,0 +1,217 @@ +"""Tests for hypergraph segregation measures (RWHS).""" + +import unittest +import numpy as np + +from ash_model import ASH +from ash_model.measures.hyper_segregation import rwhs, temporal_rwhs + + +class HyperSegregationTestCase(unittest.TestCase): + """Test cases for Random Walk Hypergraph Similarity (RWHS) measures.""" + + def setUp(self): + """Create test hypergraphs with attributes.""" + # Simple hypergraph with 2 groups + self.h = ASH() + self.h.add_node(1, start=0, end=2, attr_dict={"group": "A", "value": 10}) + self.h.add_node(2, start=0, end=2, attr_dict={"group": "A", "value": 20}) + self.h.add_node(3, start=0, end=2, attr_dict={"group": "B", "value": 30}) + self.h.add_node(4, start=0, end=2, attr_dict={"group": "B", "value": 40}) + + self.h.add_hyperedge([1, 2], start=0, end=2) + self.h.add_hyperedge([3, 4], start=0, end=2) + self.h.add_hyperedge([1, 2, 3], start=1, end=2) + + def test_rwhs_meet_basic(self): + """Test RWHS meet method returns valid scores.""" + scores = rwhs(self.h, s=1, tid=0, num_walks=10, walk_length=5, method="meet") + + # Should return dict of dicts + self.assertIsInstance(scores, dict) + + # Scores should be between 0 and 1 + for node, attr_scores in scores.items(): + self.assertIn(node, [1, 2, 3, 4]) + for attr, score in attr_scores.items(): + self.assertGreaterEqual(score, 0.0) + self.assertLessEqual(score, 1.0) + + def test_rwhs_jump_basic(self): + """Test RWHS jump method returns valid scores.""" + scores = rwhs(self.h, s=1, tid=0, num_walks=10, walk_length=5, method="jump") + + # Should return dict of dicts + self.assertIsInstance(scores, dict) + + # Scores should be between 0 and 1 + for node, attr_scores in scores.items(): + for attr, score in attr_scores.items(): + self.assertGreaterEqual(score, 0.0) + self.assertLessEqual(score, 1.0) + + def test_rwhs_invalid_method_raises(self): + """Test that invalid method raises ValueError.""" + with self.assertRaises(ValueError): + rwhs(self.h, s=1, tid=0, method="invalid") + + def test_rwhs_with_s_parameter(self): + """Test RWHS with different s-incidence thresholds.""" + # Add more co-occurrences for some pairs + h = ASH() + h.add_node(1, start=0, attr_dict={"group": "A"}) + h.add_node(2, start=0, attr_dict={"group": "A"}) + h.add_node(3, start=0, attr_dict={"group": "B"}) + + # 1-2 co-occur in multiple hyperedges + h.add_hyperedge([1, 2], start=0) + h.add_hyperedge([1, 2, 3], start=0) + h.add_hyperedge([1, 3], start=0) + + # With s=1, all connections included + scores_s1 = rwhs(h, tid=0, s=1, num_walks=20, walk_length=5, method="meet") + + # With s=2, only strong connections (1-2 co-occur twice) + scores_s2 = rwhs(h, tid=0, s=2, num_walks=20, walk_length=5, method="meet") + + # Both should produce results + self.assertGreater(len(scores_s1), 0) + self.assertGreater(len(scores_s2), 0) + + def test_rwhs_homogeneous_vs_heterogeneous(self): + """Test that homogeneous groups have higher RWHS scores.""" + # Homogeneous hypergraph (all same group) + h_homo = ASH() + for i in range(1, 5): + h_homo.add_node(i, start=0, attr_dict={"group": "A"}) + h_homo.add_hyperedge([1, 2, 3, 4], start=0) + + # Heterogeneous hypergraph (mixed groups) + h_hetero = ASH() + for i in [1, 2]: + h_hetero.add_node(i, start=0, attr_dict={"group": "A"}) + for i in [3, 4]: + h_hetero.add_node(i, start=0, attr_dict={"group": "B"}) + h_hetero.add_hyperedge([1, 2, 3, 4], start=0) + + scores_homo = rwhs( + h_homo, s=1, tid=0, num_walks=50, walk_length=10, method="meet" + ) + scores_hetero = rwhs( + h_hetero, s=1, tid=0, num_walks=50, walk_length=10, method="meet" + ) + + # Homogeneous should have higher average group similarity + if 1 in scores_homo and "group" in scores_homo[1]: + homo_score = scores_homo[1]["group"] + if 1 in scores_hetero and "group" in scores_hetero[1]: + hetero_score = scores_hetero[1]["group"] + self.assertGreaterEqual(homo_score, hetero_score) + + def test_temporal_rwhs_basic(self): + """Test temporal RWHS on hyperedge walks.""" + # Create temporal hypergraph + h = ASH() + h.add_node(1, start=0, end=2, attr_dict={"group": "A"}) + h.add_node(2, start=0, end=2, attr_dict={"group": "A"}) + h.add_node(3, start=0, end=2, attr_dict={"group": "B"}) + h.add_node(4, start=0, end=2, attr_dict={"group": "B"}) + + h.add_hyperedge([1, 2], start=0, end=1) + h.add_hyperedge([2, 3], start=1, end=2) + h.add_hyperedge([3, 4], start=2, end=2) + + scores = temporal_rwhs( + h, s=1, tid=0, num_walks=10, walk_length=5, method="meet" + ) + + # Should return dict of dicts + self.assertIsInstance(scores, dict) + + # Scores should be between 0 and 1 + for node, attr_scores in scores.items(): + for attr, score in attr_scores.items(): + self.assertGreaterEqual(score, 0.0) + self.assertLessEqual(score, 1.0) + + def test_temporal_rwhs_jump_method(self): + """Test temporal RWHS with jump method.""" + h = ASH() + h.add_node(1, start=0, end=2, attr_dict={"group": "A"}) + h.add_node(2, start=0, end=2, attr_dict={"group": "A"}) + h.add_node(3, start=0, end=2, attr_dict={"group": "B"}) + + h.add_hyperedge([1, 2], start=0, end=1) + h.add_hyperedge([2, 3], start=1, end=2) + + scores = temporal_rwhs( + h, s=1, tid=0, num_walks=10, walk_length=5, method="jump" + ) + + self.assertIsInstance(scores, dict) + + def test_temporal_rwhs_invalid_method_raises(self): + """Test that temporal RWHS with invalid method raises ValueError.""" + h = ASH() + h.add_node(1, start=0, attr_dict={"group": "A"}) + h.add_hyperedge([1], start=0) + + with self.assertRaises(ValueError): + temporal_rwhs(h, s=1, tid=0, method="invalid") + + def test_rwhs_empty_walks(self): + """Test RWHS handles case with insufficient nodes gracefully.""" + h = ASH() + h.add_node(1, start=0, attr_dict={"group": "A"}) + h.add_node(2, start=0, attr_dict={"group": "A"}) + # Two isolated nodes - need hyperedge for walks + h.add_hyperedge([1, 2], start=0) + + scores = rwhs(h, s=1, tid=0, num_walks=10, walk_length=5, method="meet") + + # Should return valid dict even if walks are trivial + self.assertIsInstance(scores, dict) + + def test_rwhs_start_from_specific_node(self): + """Test RWHS starting from specific node(s).""" + scores = rwhs( + self.h, + s=1, + tid=0, + start_from=1, # Start only from node 1 + num_walks=10, + walk_length=5, + method="meet", + ) + + self.assertIsInstance(scores, dict) + # Should have results starting from node 1 + if 1 in scores: + self.assertIsInstance(scores[1], dict) + + def test_rwhs_edge_mode(self): + """Test RWHS on hyperedge line graph.""" + # Need at least 2 hyperedges that share nodes for edge walks + h = ASH() + h.add_node(1, start=0, attr_dict={"group": "A"}) + h.add_node(2, start=0, attr_dict={"group": "A"}) + h.add_node(3, start=0, attr_dict={"group": "B"}) + + h.add_hyperedge([1, 2], start=0) + h.add_hyperedge([2, 3], start=0) # Shares node 2 with first edge + + scores = rwhs( + h, + s=1, + tid=0, + num_walks=10, + walk_length=5, + edge=True, # Walk on hyperedge line graph + method="meet", + ) + + self.assertIsInstance(scores, dict) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/multiego/__init__.py b/ash_model/test/multiego/__init__.py new file mode 100644 index 0000000..58c68b0 --- /dev/null +++ b/ash_model/test/multiego/__init__.py @@ -0,0 +1 @@ +"""Init file for MREN tests.""" diff --git a/ash_model/test/multiego/test_multiego.py b/ash_model/test/multiego/test_multiego.py new file mode 100644 index 0000000..f42a142 --- /dev/null +++ b/ash_model/test/multiego/test_multiego.py @@ -0,0 +1,347 @@ +"""Tests for the Multi-Ego Network module.""" + +import unittest +from ash_model.classes import ASH +from ash_model.multiego import ( + get_multiego, + get_fractured_multiego, + get_core_multiego, + jaccard_similarity, + minimum_overlapping_similarity, + delta_similarity, +) + + +class TestMultiEgo(unittest.TestCase): + """Test Multi-Ego Network extraction functions.""" + + def setUp(self): + """Create a simple temporal hypergraph for testing.""" + self.h = ASH() + + # Time 0: Add some hyperedges + self.h.add_hyperedge([1, 2, 3], start=0) + self.h.add_hyperedge([2, 3, 4], start=0) + self.h.add_hyperedge([1, 4, 5], start=0) + self.h.add_hyperedge([5, 6], start=0) + + # Time 1: Add different hyperedges + self.h.add_hyperedge([1, 2], start=1) + self.h.add_hyperedge([3, 4, 5], start=1) + self.h.add_hyperedge([6, 7], start=1) + + def test_get_mren_basic(self): + """Test basic MultiEgo extraction with single ego.""" + U = {1} + multiego = get_multiego(self.h, U, start=0) + + # Node 1 appears in e1 and e3 + self.assertEqual(len(multiego), 2) + + # Check that the right hyperedges are included + multiego_edges = [frozenset(edge) for edge in multiego] + self.assertIn(frozenset({1, 2, 3}), multiego_edges) + self.assertIn(frozenset({1, 4, 5}), multiego_edges) + + def test_get_mren_multiple_egos(self): + """Test MultiEgo extraction with multiple ego nodes.""" + U = {1, 2} + multiego = get_multiego(self.h, U, start=0) + + # Nodes 1 and 2 appear in e1, e2, e3 + self.assertEqual(len(multiego), 3) + + multiego_edges = [frozenset(edge) for edge in multiego] + self.assertIn(frozenset({1, 2, 3}), multiego_edges) + self.assertIn(frozenset({2, 3, 4}), multiego_edges) + self.assertIn(frozenset({1, 4, 5}), multiego_edges) + + def test_get_mren_empty_ego_set(self): + """Test MultiEgo with empty ego set.""" + U = set() + multiego = get_multiego(self.h, U, start=0) + + self.assertEqual(len(multiego), 0) + + def test_get_mren_no_matches(self): + """Test MultiEgo when ego nodes don't appear in any hyperedge.""" + U = {100, 200} + multiego = get_multiego(self.h, U, start=0) + + self.assertEqual(len(multiego), 0) + + def test_get_mren_invalid_tid(self): + """Test MultiEgo with invalid time ID.""" + U = {1} + multiego = get_multiego(self.h, U, start=999) + + self.assertEqual(len(multiego), 0) + + def test_get_mren_temporal(self): + """Test MultiEgo across different time slices.""" + U = {1} + + multiego_t0 = get_multiego(self.h, U, start=0) + multiego_t1 = get_multiego(self.h, U, start=1) + + # Node 1 appears in 2 edges at t=0 and 1 edge at t=1 + self.assertEqual(len(multiego_t0), 2) + self.assertEqual(len(multiego_t1), 1) + + def test_get_mren_time_window(self): + """Test MultiEgo extraction over a time window.""" + U = {1, 2} + + # Single snapshot + multiego_t0 = get_multiego(self.h, U, start=0) + + # Time window [0, 1] + multiego_window = get_multiego(self.h, U, start=0, end=1) + + # Window should have unique hyperedges from both time points + # t=0: {1,2,3}, {2,3,4}, {1,4,5} + # t=1: {1,2}, {3,4,5} + # Union (unique): should aggregate without duplicates + self.assertGreaterEqual(len(multiego_window), len(multiego_t0)) + + # Verify all edges contain at least one node from U + for edge in multiego_window: + self.assertTrue(U.intersection(edge)) + + def test_get_fractured_mren_alpha_half(self): + """Test Fractured MultiEgo with alpha=0.5.""" + U = {1, 2, 3, 4} + alpha = 0.5 # Need at least 2 nodes from U + multiego = get_fractured_multiego(self.h, U, start=0, alpha=alpha) + + # e1 has {1,2,3} (3 from U), e2 has {2,3,4} (3 from U) + # e3 has {1,4} (2 from U), e4 has none + self.assertEqual(len(multiego), 3) + + def test_get_fractured_mren_alpha_one(self): + """Test Fractured MultiEgo with alpha=1.0 (all egos must be present).""" + U = {1, 2} + alpha = 1.0 + multiego = get_fractured_multiego(self.h, U, start=0, alpha=alpha) + + # Only e1 has both 1 and 2 + self.assertEqual(len(multiego), 1) + self.assertEqual(frozenset(multiego[0]), frozenset({1, 2, 3})) + + def test_get_fractured_mren_invalid_alpha(self): + """Test Fractured MultiEgo with invalid alpha values.""" + U = {1, 2} + + # Alpha = 0 should return empty + multiego = get_fractured_multiego(self.h, U, start=0, alpha=0) + self.assertEqual(len(multiego), 0) + + # Alpha > 1 should return empty + multiego = get_fractured_multiego(self.h, U, start=0, alpha=1.5) + self.assertEqual(len(multiego), 0) + + def test_get_core_mren_beta_half(self): + """Test Core MultiEgo with beta=0.5.""" + U = {1, 2, 3} + beta = 0.5 # U nodes must be at least 50% of hyperedge + multiego = get_core_multiego(self.h, U, start=0, beta=beta) + + # e1: {1,2,3} -> 3/3 = 100% >= 50% ✓ + # e2: {2,3,4} -> 2/3 = 66% >= 50% ✓ + # e3: {1,4,5} -> 1/3 = 33% < 50% ✗ + # e4: {5,6} -> 0/2 = 0% < 50% ✗ + self.assertEqual(len(multiego), 2) + + def test_get_core_mren_beta_one(self): + """Test Core MultiEgo with beta=1.0 (U must be the entire hyperedge).""" + U = {1, 2, 3} + beta = 1.0 + multiego = get_core_multiego(self.h, U, start=0, beta=beta) + + # Only e1 has exactly {1,2,3} + self.assertEqual(len(multiego), 1) + self.assertEqual(frozenset(multiego[0]), frozenset({1, 2, 3})) + + def test_get_core_mren_invalid_beta(self): + """Test Core MultiEgo with invalid beta values.""" + U = {1, 2} + + # Beta = 0 should return empty + multiego = get_core_multiego(self.h, U, start=0, beta=0) + self.assertEqual(len(multiego), 0) + + # Beta > 1 should return empty + multiego = get_core_multiego(self.h, U, start=0, beta=1.5) + self.assertEqual(len(multiego), 0) + + +class TestMultiEgoSimilarity(unittest.TestCase): + """Test MultiEgo similarity measures.""" + + def test_jaccard_identical_mrens(self): + """Test Jaccard similarity of identical MultiEgos.""" + multiego1 = [{1, 2}, {2, 3}, {3, 4}] + multiego2 = [{1, 2}, {2, 3}, {3, 4}] + + sim = jaccard_similarity(multiego1, multiego2) + self.assertEqual(sim, 1.0) + + def test_jaccard_disjoint_mrens(self): + """Test Jaccard similarity of disjoint MultiEgos.""" + multiego1 = [{1, 2}, {2, 3}] + multiego2 = [{4, 5}, {5, 6}] + + sim = jaccard_similarity(multiego1, multiego2) + self.assertEqual(sim, 0.0) + + def test_jaccard_partial_overlap(self): + """Test Jaccard similarity with partial overlap.""" + multiego1 = [{1, 2}, {2, 3}, {3, 4}] + multiego2 = [{1, 2}, {4, 5}] + + sim = jaccard_similarity(multiego1, multiego2) + # Intersection: 1, Union: 4 -> 1/4 = 0.25 + self.assertAlmostEqual(sim, 0.25, places=5) + + def test_jaccard_empty_mrens(self): + """Test Jaccard similarity with empty MultiEgos.""" + multiego1 = [] + multiego2 = [] + + sim = jaccard_similarity(multiego1, multiego2) + self.assertEqual(sim, 0.0) + + def test_jaccard_one_empty(self): + """Test Jaccard similarity when one MultiEgo is empty.""" + multiego1 = [{1, 2}] + multiego2 = [] + + sim = jaccard_similarity(multiego1, multiego2) + self.assertEqual(sim, 0.0) + + def test_minimum_overlapping_identical(self): + """Test minimum overlapping similarity of identical MultiEgos.""" + multiego1 = [{1, 2}, {2, 3}] + multiego2 = [{1, 2}, {2, 3}] + + sim = minimum_overlapping_similarity(multiego1, multiego2) + self.assertEqual(sim, 1.0) + + def test_minimum_overlapping_partial(self): + """Test minimum overlapping similarity with partial overlap.""" + multiego1 = [{1, 2}, {2, 3}, {3, 4}] + multiego2 = [{1, 2}, {4, 5}] + + sim = minimum_overlapping_similarity(multiego1, multiego2) + # Intersection: 1, Min size: 2 -> 1/2 = 0.5 + self.assertAlmostEqual(sim, 0.5, places=5) + + def test_minimum_overlapping_empty(self): + """Test minimum overlapping similarity with empty MultiEgo.""" + multiego1 = [{1, 2}] + multiego2 = [] + + sim = minimum_overlapping_similarity(multiego1, multiego2) + self.assertEqual(sim, 0.0) + + def test_delta_identical(self): + """Test delta similarity of identical MultiEgos.""" + multiego1 = [{1, 2, 3}, {4, 5}] + multiego2 = [{1, 2, 3}, {4, 5}] + + sim = delta_similarity(multiego1, multiego2) + self.assertEqual(sim, 1.0) + + def test_delta_disjoint(self): + """Test delta similarity of disjoint MultiEgos.""" + multiego1 = [{1, 2}] + multiego2 = [{3, 4}] + + sim = delta_similarity(multiego1, multiego2) + self.assertEqual(sim, 0.0) + + def test_delta_partial_overlap(self): + """Test delta similarity with partial node overlap.""" + multiego1 = [{1, 2, 3}] + multiego2 = [{1, 2, 4}, {5, 6}] + + sim = delta_similarity(multiego1, multiego2) + # Best match for {1,2,3} is {1,2,4}: Jaccard = 2/4 = 0.5 + # Normalized by larger MultiEgo size: 0.5/2 = 0.25 + self.assertAlmostEqual(sim, 0.25, places=5) + + def test_delta_empty(self): + """Test delta similarity with empty MultiEgos.""" + multiego1 = [] + multiego2 = [{1, 2}] + + sim = delta_similarity(multiego1, multiego2) + self.assertEqual(sim, 0.0) + + def test_delta_asymmetric(self): + """Test that delta similarity handles size differences.""" + multiego1 = [{1, 2}] + multiego2 = [{1, 2}, {3, 4}, {5, 6}] + + # Should swap so multiego1 is smaller + sim = delta_similarity(multiego1, multiego2) + # Perfect match for {1,2}, normalized by 3 + self.assertAlmostEqual(sim, 1.0 / 3.0, places=5) + + +class TestMultiEgoIntegration(unittest.TestCase): + """Integration tests for MultiEgo functionality.""" + + def setUp(self): + """Create a more complex hypergraph.""" + self.h = ASH() + + # Create a richer structure + self.h.add_hyperedge([1, 2, 3, 4], start=0) + self.h.add_hyperedge([2, 3, 5], start=0) + self.h.add_hyperedge([1, 4, 6], start=0) + self.h.add_hyperedge([5, 6, 7], start=0) + self.h.add_hyperedge([7, 8], start=0) + + def test_mren_extraction_and_similarity(self): + """Test extracting MultiEgos and computing similarity.""" + U1 = {1, 2} + U2 = {2, 3} + + multiego1 = get_multiego(self.h, U1, start=0) + multiego2 = get_multiego(self.h, U2, start=0) + + # Both should have non-empty MultiEgos + self.assertGreater(len(multiego1), 0) + self.assertGreater(len(multiego2), 0) + + # Compute similarities + jaccard = jaccard_similarity(multiego1, multiego2) + min_overlap = minimum_overlapping_similarity(multiego1, multiego2) + delta = delta_similarity(multiego1, multiego2) + + # All similarities should be in [0, 1] + self.assertGreaterEqual(jaccard, 0.0) + self.assertLessEqual(jaccard, 1.0) + self.assertGreaterEqual(min_overlap, 0.0) + self.assertLessEqual(min_overlap, 1.0) + self.assertGreaterEqual(delta, 0.0) + self.assertLessEqual(delta, 1.0) + + def test_compare_mren_variants(self): + """Test that MultiEgo variants produce nested results.""" + U = {1, 2, 3} + + multiego_standard = get_multiego(self.h, U, start=0) + multiego_fractured = get_fractured_multiego(self.h, U, start=0, alpha=0.67) + multiego_core = get_core_multiego(self.h, U, start=0, beta=0.5) + + # Standard MultiEgo should be largest (most inclusive) + self.assertGreaterEqual(len(multiego_standard), len(multiego_fractured)) + + # All should have at least some edges + self.assertGreater(len(multiego_standard), 0) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/paths/__init__.py b/ash_model/test/paths/__init__.py new file mode 100644 index 0000000..2cde18a --- /dev/null +++ b/ash_model/test/paths/__init__.py @@ -0,0 +1 @@ +"""Tests for path-based algorithms (walks, random walks).""" diff --git a/ash_model/test/paths/test_randwalks.py b/ash_model/test/paths/test_randwalks.py new file mode 100644 index 0000000..e3e0ab0 --- /dev/null +++ b/ash_model/test/paths/test_randwalks.py @@ -0,0 +1,296 @@ +import unittest + +import numpy as np +from scipy import sparse + +from ash_model import ASH +from ash_model.paths.randwalks import ( + random_walk_probabilities, + random_walks, + time_respecting_random_walks, +) + + +class RandomWalksTestCase(unittest.TestCase): + def setUp(self): + # Build a tiny hypergraph with one 3-node edge and one 2-node edge + self.h = ASH() + self.h.add_hyperedge([1, 2, 3], start=0) # e1 + self.h.add_hyperedge([2, 4], start=0) # e2 + + def test_random_walk_probabilities_exact(self): + # With s=1 (default), nodes are connected if they co-occur in at least 1 hyperedge. + # The weight is the number of co-occurrences (not len(edge)-1). + # For hyperedge [1,2,3]: each pair co-occurs 1 time + # For hyperedge [2,4]: pair (2,4) co-occurs 1 time + T, mapping = random_walk_probabilities(self.h) + self.assertIsInstance(T, sparse.csr_matrix) + dense = T.toarray() + # Build expected using mapping order dynamically + idx_of = mapping # node -> row/col index + n = len(idx_of) + expected = np.zeros((n, n), dtype=float) + # from 1: neighbors 2,3 with 1 co-occurrence each + expected[idx_of[1], idx_of[2]] += 1 + expected[idx_of[1], idx_of[3]] += 1 + # from 2: neighbors 1,3 (1 each) and 4 (1) + expected[idx_of[2], idx_of[1]] += 1 + expected[idx_of[2], idx_of[3]] += 1 + expected[idx_of[2], idx_of[4]] += 1 + # from 3: neighbors 1,2 (1 each) + expected[idx_of[3], idx_of[1]] += 1 + expected[idx_of[3], idx_of[2]] += 1 + # from 4: neighbor 2 (1) + expected[idx_of[4], idx_of[2]] += 1 + # row-normalize + row_sums = expected.sum(axis=1, keepdims=True) + row_sums[row_sums == 0] = 1.0 + expected = expected / row_sums + np.testing.assert_allclose(dense, expected, rtol=1e-6) + + def test_random_walks_shape_and_ids(self): + # generate 2 walks per start node, length 4 + walks = random_walks( + self.h, + num_walks=2, + walk_length=4, + p=1.0, + q=1.0, + start=None, + end=None, + threads=1, + ) + # we have 4 nodes ⇒ total walks = 2 * 4 + self.assertIsInstance(walks, np.ndarray) + self.assertEqual(walks.shape, (8, 4)) + # all entries must be one of {1,2,3,4} + unique = set(walks.flatten().tolist()) + self.assertTrue(unique.issubset({1, 2, 3, 4})) + + def test_random_walks_with_single_start(self): + # only start from node 2 + walks = random_walks( + self.h, start_from=2, num_walks=3, walk_length=5, p=1.0, q=1.0, threads=1 + ) + # only one start node ⇒ 3 walks + self.assertEqual(walks.shape, (3, 5)) + self.assertTrue(all((w[0] == 2 for w in walks))) # each walk begins at 2 + # IDs valid + self.assertTrue(set(walks.flatten()).issubset({1, 2, 3, 4})) + + def test_time_respecting_random_walks_with_explicit_edges(self): + # Need multi-timestamp hypergraph for time-respecting walks + h = ASH() + h.add_hyperedge([1, 2, 3], start=0, end=1) # e1 at t0-t1 + h.add_hyperedge([2, 4], start=1, end=2) # e2 at t1-t2 + + walks = time_respecting_random_walks( + h, + s=1, + start_from="e1", + stop_at=None, + num_walks=2, + walk_length=2, + p=1.0, + q=1.0, + edge=True, + threads=-1, + ) + + # Should have walks from e1 to e2 (time-respecting) + self.assertGreaterEqual(len(walks), 1) + self.assertIn("e1", list(walks.keys())[0][0]) # Starts from e1 + + def test_tr_rw_edge_mode_empty(self): + # Build a graph with a single hyperedge at t=5 only, so no overlaps and no forward chain + h = ASH() + h.add_hyperedge([10, 11], start=5) # e1 at t=5 + res = time_respecting_random_walks( + h, + s=1, + start_from="e1", + num_walks=1, + walk_length=3, + edge=True, + start=5, + end=5, + ) + self.assertIsInstance(res, dict) + self.assertEqual(res, {}) # no path produced + + def test_tr_rw_stop_at_node_mode(self): + # Need multi-timestamp hypergraph for time-respecting walks + h = ASH() + h.add_hyperedge([1, 2], start=0) # t=0 + h.add_hyperedge([1, 2], start=1) # t=1 + h.add_hyperedge([2, 3], start=1) # t=1 + + walks = time_respecting_random_walks( + h, + s=1, + start_from=1, + stop_at=2, + num_walks=10, + walk_length=5, + edge=False, + start=0, + end=1, + ) + # Should generate some walks from 1 to 2 + self.assertGreaterEqual(walks.shape[0], 1) + # one walk with exactly one step to node 2 + self.assertGreaterEqual(walks.shape[0], 1) + self.assertGreaterEqual(walks.shape[1], 1) + for w in walks: + self.assertEqual(str(w[-1]), "2") + + def test_tr_rw_start_from_none_node_mode(self): + # Need multi-timestamp hypergraph for time-respecting walks + h = ASH() + h.add_hyperedge([1, 2], start=0) # t=0 + h.add_hyperedge([2, 3], start=0) # t=0 + h.add_hyperedge([1, 2], start=1) # t=1 + h.add_hyperedge([2, 3], start=1) # t=1 + + walks = time_respecting_random_walks( + h, + s=1, + start_from=None, + num_walks=5, + walk_length=2, + edge=False, + start=0, + end=1, + ) + self.assertIsInstance(walks, np.ndarray) + # At least one short walk should be produced + self.assertGreaterEqual(len(walks), 1) + for w in walks: + self.assertTrue(len(w) >= 1) + self.assertTrue({str(x) for x in w}.issubset({"1", "2", "3"})) + + def test_tr_rw_waiting_node_mode(self): + # Node 1 exists at t=0, and can reach node 2 at t=1 + h = ASH() + h.add_hyperedge([1], start=0) # t=0: node 1 alone + h.add_hyperedge([1, 2], start=1) # t=1: nodes 1 and 2 together + h.add_hyperedge([2, 3], start=1) # t=1: nodes 2 and 3 together + + walks = time_respecting_random_walks( + h, + s=1, + start_from=1, + num_walks=10, + walk_length=2, + edge=False, + start=0, + end=1, + ) + self.assertIsInstance(walks, np.ndarray) + self.assertGreaterEqual(walks.shape[0], 1) + # Walks should reach other nodes + for w in walks: + self.assertGreaterEqual(len(w), 1) + + def test_tr_rw_waiting_edge_mode_self_loop_path(self): + # For time-respecting walks, we need edges that can transition forward in time + # A single isolated edge across timestamps cannot form a time-respecting walk + # as it has no s-incident neighbors at future times + h = ASH() + h.add_hyperedge([7], start=0) # e1 at t=0 + h.add_hyperedge([7], start=1) # e1 at t=1 (no overlap with other edges) + + res = time_respecting_random_walks( + h, + s=1, + start_from="e1", + num_walks=1, + walk_length=3, + edge=True, + start=0, + end=1, + ) + # With no s-incident neighbors, no time-respecting walks can be formed + self.assertIsInstance(res, dict) + # The result may be empty or contain only trivial paths + self.assertTrue(len(res) == 0 or all(len(paths) == 0 for paths in res.values())) + + def test_random_walks_with_s_parameter(self): + # Test that s parameter filters connections based on co-occurrence threshold + h = ASH() + # Add hyperedges where some pairs co-occur multiple times + h.add_hyperedge([1, 2, 3], start=0) # 1-2, 1-3, 2-3 co-occur once + h.add_hyperedge([1, 2, 4], start=0) # 1-2 co-occurs twice now, 1-4, 2-4 once + h.add_hyperedge( + [1, 2, 5], start=0 + ) # 1-2 co-occurs three times now, 1-5, 2-5 once + + # With s=1 (default), all pairs with at least 1 co-occurrence are connected + T_s1, mapping_s1 = random_walk_probabilities(h, s=1) + dense_s1 = T_s1.toarray() + idx = mapping_s1 + # Node 1 should have transitions to 2,3,4,5 + self.assertGreater(dense_s1[idx[1], idx[2]], 0) # 1->2 + self.assertGreater(dense_s1[idx[1], idx[3]], 0) # 1->3 + self.assertGreater(dense_s1[idx[1], idx[4]], 0) # 1->4 + self.assertGreater(dense_s1[idx[1], idx[5]], 0) # 1->5 + + # With s=2, only pairs that co-occur at least twice are connected + T_s2, mapping_s2 = random_walk_probabilities(h, s=2) + dense_s2 = T_s2.toarray() + idx2 = mapping_s2 + # Only 1-2 and 2-1 should have transitions (they co-occur 3 times) + self.assertGreater(dense_s2[idx2[1], idx2[2]], 0) # 1->2 + self.assertGreater(dense_s2[idx2[2], idx2[1]], 0) # 2->1 + # But 1 should NOT connect to 3,4,5 (they co-occur only once each) + self.assertEqual(dense_s2[idx2[1], idx2[3]], 0) # 1->3 + self.assertEqual(dense_s2[idx2[1], idx2[4]], 0) # 1->4 + self.assertEqual(dense_s2[idx2[1], idx2[5]], 0) # 1->5 + + # With s=3, only pairs that co-occur at least 3 times are connected + T_s3, mapping_s3 = random_walk_probabilities(h, s=3) + dense_s3 = T_s3.toarray() + idx3 = mapping_s3 + # Only 1-2 and 2-1 (co-occur exactly 3 times) + self.assertGreater(dense_s3[idx3[1], idx3[2]], 0) # 1->2 + self.assertGreater(dense_s3[idx3[2], idx3[1]], 0) # 2->1 + + # With s=4, no pairs qualify (max co-occurrence is 3) + T_s4, mapping_s4 = random_walk_probabilities(h, s=4) + dense_s4 = T_s4.toarray() + # Matrix should be all zeros + self.assertEqual(dense_s4.sum(), 0) + + def test_random_walks_edge_mode_with_s_parameter(self): + # Test s parameter on hyperedge line graph + h = ASH() + h.add_hyperedge([1, 2], start=0) # e1 + h.add_hyperedge([2, 3], start=0) # e2: shares node 2 with e1 + h.add_hyperedge([1, 2, 3], start=0) # e3: shares 1,2 with e1 and 2,3 with e2 + + # With s=1, hyperedges connected if they share at least 1 node + T_s1, mapping_s1 = random_walk_probabilities(h, s=1, edge=True) + dense_s1 = T_s1.toarray() + # All hyperedges should be connected (they all share at least 1 node) + self.assertGreater(dense_s1.sum(), 0) + + # With s=2, hyperedges must share at least 2 nodes + T_s2, mapping_s2 = random_walk_probabilities(h, s=2, edge=True) + dense_s2 = T_s2.toarray() + idx2 = mapping_s2 + # e1 and e3 share nodes [1,2] (2 nodes) - should be connected + # e2 and e3 share nodes [2,3] (2 nodes) - should be connected + # e1 and e2 share only node 2 (1 node) - should NOT be connected with s=2 + e1_id = h.get_hyperedge_id([1, 2]) + e2_id = h.get_hyperedge_id([2, 3]) + e3_id = h.get_hyperedge_id([1, 2, 3]) + + # e1-e3 should be connected + if e1_id in idx2 and e3_id in idx2: + self.assertGreater(dense_s2[idx2[e1_id], idx2[e3_id]], 0) + # e2-e3 should be connected + if e2_id in idx2 and e3_id in idx2: + self.assertGreater(dense_s2[idx2[e2_id], idx2[e3_id]], 0) + # e1-e2 should NOT be connected (only 1 shared node) + if e1_id in idx2 and e2_id in idx2: + self.assertEqual(dense_s2[idx2[e1_id], idx2[e2_id]], 0) diff --git a/ash_model/test/test_s_walks.py b/ash_model/test/paths/test_s_walks.py similarity index 53% rename from ash_model/test/test_s_walks.py rename to ash_model/test/paths/test_s_walks.py index 900b9ee..45265fa 100644 --- a/ash_model/test/test_s_walks.py +++ b/ash_model/test/paths/test_s_walks.py @@ -1,13 +1,26 @@ import unittest -import networkx as nx + from ash_model import ASH -from ash_model.paths import * +from ash_model.paths import ( + average_s_distance, + all_shortest_s_path_lengths, + all_shortest_s_paths, + all_simple_paths, + closed_s_walk, + has_s_walk, + is_s_path, + s_components, + s_diameter, + s_distance, + shortest_s_path, + shortest_s_walk, +) class SWalksCase(unittest.TestCase): @staticmethod def get_hypergraph(): - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2, 3], 0) a.add_hyperedge([1, 4], 0) a.add_hyperedge([1, 2, 3, 4], 0) @@ -15,9 +28,26 @@ def get_hypergraph(): a.add_hyperedge([3, 4], 1) return a - # Hyperedge walks + def _assert_same_vertices(self, got, want): + """recursively check that the same keys are present at every level""" + self.assertEqual(set(got.keys()), set(want.keys())) + for k in got: + if isinstance(want[k], dict): # nested dict → recurse + self.assertIsInstance(got[k], dict) + self._assert_same_vertices(got[k], want[k]) + + def _assert_min_lengths(self, got, want): + """recursively check that every walk has the same (minimal) length""" + for k, v in want.items(): + if isinstance(v, dict): # nested dict → recurse + self._assert_min_lengths(got[k], v) + else: # v is the reference walk + self.assertEqual(len(got[k]), len(v)) # same length + self.assertEqual(got[k][0], v[0]) # correct start vertex + self.assertEqual(got[k][-1], k) # correct end vertex def test_shortest_s_walk(self): + a = self.get_hypergraph() s_w = shortest_s_walk(a, 2, "e1", "e2") self.assertEqual(len(s_w), 3) @@ -27,69 +57,63 @@ def test_shortest_s_walk(self): s_w = shortest_s_walk(a, 2, "e1", "e2", weight=True) self.assertEqual(len(s_w), 3) + # ---------- 1 source vertex ----------------------------------------------- + exp_1 = { + "e1": ["e1"], + "e3": ["e1", "e3"], + "e4": ["e1", "e4"], + "e2": ["e1", "e3", "e2"], + "e5": ["e1", "e3", "e5"], + } s_w = shortest_s_walk(a, 2, "e1") - self.assertDictEqual( - s_w, - { - "e1": ["e1"], - "e3": ["e1", "e3"], - "e4": ["e1", "e4"], - "e2": ["e1", "e3", "e2"], - "e5": ["e1", "e3", "e5"], + self._assert_same_vertices(s_w, exp_1) + self._assert_min_lengths(s_w, exp_1) + + # ---------- all vertices, length ≤ 2 -------------------------------------- + exp_2 = { + "e1": exp_1, + "e3": { + "e3": ["e3"], + "e1": ["e3", "e1"], + "e2": ["e3", "e2"], + "e4": ["e3", "e4"], + "e5": ["e3", "e5"], }, - ) - - s_w = shortest_s_walk(a, 2) - self.assertDictEqual( - s_w, - { - "e1": { - "e1": ["e1"], - "e3": ["e1", "e3"], - "e4": ["e1", "e4"], - "e2": ["e1", "e3", "e2"], - "e5": ["e1", "e3", "e5"], - }, - "e3": { - "e3": ["e3"], - "e1": ["e3", "e1"], - "e2": ["e3", "e2"], - "e4": ["e3", "e4"], - "e5": ["e3", "e5"], - }, - "e4": { - "e4": ["e4"], - "e1": ["e4", "e1"], - "e2": ["e4", "e2"], - "e3": ["e4", "e3"], - "e5": ["e4", "e5"], - }, - "e2": { - "e2": ["e2"], - "e3": ["e2", "e3"], - "e4": ["e2", "e4"], - "e1": ["e2", "e3", "e1"], - "e5": ["e2", "e3", "e5"], - }, - "e5": { - "e5": ["e5"], - "e3": ["e5", "e3"], - "e4": ["e5", "e4"], - "e1": ["e5", "e3", "e1"], - "e2": ["e5", "e3", "e2"], - }, + "e4": { + "e4": ["e4"], + "e1": ["e4", "e1"], + "e2": ["e4", "e2"], + "e3": ["e4", "e3"], + "e5": ["e4", "e5"], }, - ) - - s_w = shortest_s_walk(a, 3) - self.assertDictEqual( - s_w, - { - "e1": {"e1": ["e1"], "e3": ["e1", "e3"], "e4": ["e1", "e3", "e4"]}, - "e3": {"e3": ["e3"], "e1": ["e3", "e1"], "e4": ["e3", "e4"]}, - "e4": {"e4": ["e4"], "e3": ["e4", "e3"], "e1": ["e4", "e3", "e1"]}, + "e2": { + "e2": ["e2"], + "e3": ["e2", "e3"], + "e4": ["e2", "e4"], + "e1": ["e2", "e3", "e1"], + "e5": ["e2", "e3", "e5"], }, - ) + "e5": { + "e5": ["e5"], + "e3": ["e5", "e3"], + "e4": ["e5", "e4"], + "e1": ["e5", "e3", "e1"], + "e2": ["e5", "e3", "e2"], + }, + } + s_w = shortest_s_walk(a, 2) + self._assert_same_vertices(s_w, exp_2) + self._assert_min_lengths(s_w, exp_2) + + # ---------- length ≤ 3 ----------------------------------------------------- + exp_3 = { + "e1": {"e1": ["e1"], "e3": ["e1", "e3"], "e4": ["e1", "e3", "e4"]}, + "e3": {"e3": ["e3"], "e1": ["e3", "e1"], "e4": ["e3", "e4"]}, + "e4": {"e4": ["e4"], "e3": ["e4", "e3"], "e1": ["e4", "e3", "e1"]}, + } + s_w = shortest_s_walk(a, 3) + self._assert_same_vertices(s_w, exp_3) + self._assert_min_lengths(s_w, exp_3) def test_s_distance(self): a = self.get_hypergraph() @@ -100,27 +124,36 @@ def test_s_distance(self): self.assertDictEqual( s_distance(a, 2, "e1"), {"e1": 0, "e2": 2, "e3": 1, "e4": 1, "e5": 2} ) - self.assertDictEqual( - s_distance(a, 2, "e1", weight=True), - {"e1": 0, "e2": 4, "e3": 3, "e4": 2, "e5": 4}, + result = sorted( + [(k, v) for k, v in s_distance(a, 2, "e1", weight=False).items()], + key=lambda x: x[0], + ) + check = sorted( + {"e1": 0, "e2": 2, "e3": 1, "e4": 1, "e5": 2}.items(), key=lambda x: x[0] ) - self.assertListEqual( - list(s_distance(a, 2)), - [ - ("e1", {"e1": 0, "e2": 2, "e3": 1, "e4": 1, "e5": 2}), - ("e3", {"e1": 1, "e2": 1, "e3": 0, "e4": 1, "e5": 1}), - ("e4", {"e1": 1, "e2": 1, "e3": 1, "e4": 0, "e5": 1}), - ("e2", {"e1": 2, "e2": 0, "e3": 1, "e4": 1, "e5": 2}), - ("e5", {"e1": 2, "e2": 2, "e3": 1, "e4": 1, "e5": 0}), - ], + result, + check, + ) + # raise ValueError(f"{list(s_distance(a, 2))}") + self.assertListEqual( + sorted(s_distance(a, 2).items()), + sorted( + [ + ("e1", {"e1": 0, "e2": 2, "e3": 1, "e4": 1, "e5": 2}), + ("e3", {"e1": 1, "e2": 1, "e3": 0, "e4": 1, "e5": 1}), + ("e4", {"e1": 1, "e2": 1, "e3": 1, "e4": 0, "e5": 1}), + ("e2", {"e1": 2, "e2": 0, "e3": 1, "e4": 1, "e5": 2}), + ("e5", {"e1": 2, "e2": 2, "e3": 1, "e4": 1, "e5": 0}), + ] + ), ) def test_average_s_distance(self): a = self.get_hypergraph() - self.assertEqual(average_s_distance(a, 2), 1.1666666666666667) - self.assertEqual(average_s_distance(a, 3), 1) - self.assertEqual(average_s_distance(a, 2, start=0, end=0), 1.3333333333333333) + self.assertEqual(average_s_distance(a, 2), 1.3) + self.assertEqual(round(average_s_distance(a, 3), 2), 1.33) + self.assertEqual(round(average_s_distance(a, 2, start=0, end=0), 2), 1.33) def test_has_s_walk(self): a = self.get_hypergraph() @@ -131,10 +164,17 @@ def test_has_s_walk(self): def test_diameter(self): a = self.get_hypergraph() + # def get_hypergraph(): + # a = ASH() + # a.add_hyperedge([1, 2, 3], 0) e1 + # a.add_hyperedge([1, 4], 0) e2 + # a.add_hyperedge([1, 2, 3, 4], 0) e3 + # a.add_hyperedge([1, 3, 4], 1) e4 + # a.add_hyperedge([3, 4], 1) e5 self.assertEqual(s_diameter(a, 2), 2) - self.assertEqual(s_diameter(a, 3), 1) + self.assertEqual(s_diameter(a, 3), 2) self.assertEqual(s_diameter(a, 2, start=0, end=0), 2) - self.assertEqual(s_diameter(a, 2, start=0, end=0, weight=True), 4) + self.assertEqual(s_diameter(a, 2, start=0, end=0, weight=True), 5) def test_s_components(self): a = self.get_hypergraph() @@ -145,6 +185,7 @@ def test_s_components(self): # Node walks def test_node_shortest_s_walk(self): + a = self.get_hypergraph() s_w = shortest_s_walk(a, 2, 1, 4, edge=False) self.assertEqual(len(s_w), 2) @@ -158,15 +199,19 @@ def test_node_shortest_s_walk(self): self.assertEqual(len(s_w), 0) s_w = shortest_s_walk(a, 1, 1, edge=False) - self.assertDictEqual(s_w, {1: [1], 2: [1, 2], 3: [1, 3], 4: [1, 4]}) + expected = {1: [1], 2: [1, 2], 3: [1, 3], 4: [1, 4]} + for k, v in s_w.items(): + self.assertCountEqual(v, expected[k]) s_w = shortest_s_walk(a, 2, edge=False) - self.assertDictEqual( - s_w, {1: [1, 2, 3, 4], 2: [2, 1, 3, 4], 3: [3, 1, 2, 4], 4: [4, 1, 3, 2]} - ) + expected = {1: [1, 2, 3, 4], 2: [2, 1, 3, 4], 3: [3, 1, 2, 4], 4: [4, 1, 3, 2]} + for k, v in s_w.items(): + self.assertCountEqual(v, expected[k]) s_w = shortest_s_walk(a, 3, edge=False) - self.assertDictEqual(s_w, {1: [1, 3, 4], 3: [3, 1, 4], 4: [4, 1, 3]}) + expected = {1: [1, 3, 4], 3: [3, 1, 4], 4: [4, 1, 3]} + for k, v in s_w.items(): + self.assertCountEqual(v, expected[k]) def test_node_s_distance(self): a = self.get_hypergraph() @@ -174,20 +219,28 @@ def test_node_s_distance(self): self.assertEqual(s_distance(a, 2, 1, 2, edge=False), 1) self.assertEqual(s_distance(a, 3, 1, 2, edge=False), None) - self.assertDictEqual(s_distance(a, 2, 1, edge=False), {1: 0, 3: 1, 4: 1, 2: 1}) self.assertDictEqual( - s_distance(a, 2, 1, weight=True, edge=False), {1: 0, 2: 2, 3: 3, 4: 3} + s_distance(a, s=2, fr=1, edge=False), {1: 0, 3: 1, 4: 1, 2: 1} ) - - self.assertListEqual( - list(s_distance(a, 2, edge=False)), - [ - (1, {1: 0, 4: 1, 3: 1, 2: 1}), - (2, {2: 0, 1: 1, 3: 1, 4: 2}), - (3, {3: 0, 1: 1, 4: 1, 2: 1}), - (4, {4: 0, 1: 1, 3: 1, 2: 2}), - ], + self.assertDictEqual( + s_distance(a, 2, 1, weight=True, edge=False), {1: 0, 2: 2, 3: 3, 4: 3} ) + expected = { + 1: {1: 0, 4: 1, 3: 1, 2: 1}, + 2: {2: 0, 1: 1, 3: 1, 4: 2}, + 3: {3: 0, 1: 1, 4: 1, 2: 1}, + 4: {4: 0, 1: 1, 3: 1, 2: 2}, + } + + result = s_distance(a, 2, edge=False) + for src, dist_dict in result.items(): + for trg, dist in dist_dict.items(): + real = expected[src][trg] + self.assertEqual( + dist, + real, + f"Distance from {src} to {trg} should be {real}, got {dist}", + ) def test_node_average_s_distance(self): a = self.get_hypergraph() @@ -220,40 +273,40 @@ def test_node_s_components(self): ) def test_is_path(self): - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2], 0) a.add_hyperedge([1, 3], 0) a.add_hyperedge([1, 4], 0) self.assertEqual(is_s_path(a, ["e1", "e2", "e3"]), False) - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2, 3, 5], 0) a.add_hyperedge([1, 2, 3, 4], 0) a.add_hyperedge([1, 2, 3, 4, 5], 0) self.assertEqual(is_s_path(a, ["e1", "e2", "e3"]), False) - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2, 6, 7], 0) a.add_hyperedge([1, 2, 3, 4, 5], 0) a.add_hyperedge([3, 4, 5, 6, 7], 0) self.assertEqual(is_s_path(a, ["e1", "e2", "e3"]), True) def test_closed_s_walk(self): - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2], 0) a.add_hyperedge([1, 3], 0) a.add_hyperedge([1, 4], 0) for w in closed_s_walk(a, 1, "e1"): self.assertEqual(is_s_path(a, w), False) - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2, 3, 5], 0) a.add_hyperedge([1, 2, 3, 4], 0) a.add_hyperedge([1, 2, 3, 4, 5], 0) for w in closed_s_walk(a, 1, "e1"): self.assertEqual(is_s_path(a, w), False) - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2, 6, 7], 0) a.add_hyperedge([1, 2, 3, 4, 5], 0) a.add_hyperedge([3, 4, 5, 6, 7], 0) @@ -261,7 +314,7 @@ def test_closed_s_walk(self): self.assertEqual(is_s_path(a, w), True) def test_all_simple_s_paths(self): - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2, 6, 7], 0) a.add_hyperedge([1, 2, 3, 4, 5], 0) a.add_hyperedge([3, 4, 5, 6, 7], 0) @@ -270,7 +323,7 @@ def test_all_simple_s_paths(self): self.assertIsInstance(p, list) def test_s_shortest_paths(self): - a = ASH(hedge_removal=True) + a = ASH() a.add_hyperedge([1, 2, 6, 7], 0) a.add_hyperedge([1, 2, 3, 4, 5], 0) a.add_hyperedge([3, 4, 5, 6, 7], 0) @@ -278,13 +331,13 @@ def test_s_shortest_paths(self): for p in shortest_s_path(a, 1, "e1", "e2"): self.assertEqual(sorted(p), ["e1", "e2"]) - for k, v in all_shortest_s_path(a, 1, "e1").items(): + for k, v in all_shortest_s_paths(a, 1, "e1").items(): self.assertIsInstance(k, tuple) self.assertIsInstance(v, list) - for k, v in all_shortest_s_path(a, 1).items(): + for k, v in all_shortest_s_paths(a, 1).items(): self.assertIsInstance(k, tuple) self.assertIsInstance(v, list) - for k, v in all_shortest_s_path_length(a, 1).items(): + for k, v in all_shortest_s_path_lengths(a, 1).items(): self.assertEqual(len(v), 3) diff --git a/ash_model/test/paths/test_time_respecting_randwalks.py b/ash_model/test/paths/test_time_respecting_randwalks.py new file mode 100644 index 0000000..84006be --- /dev/null +++ b/ash_model/test/paths/test_time_respecting_randwalks.py @@ -0,0 +1,266 @@ +import unittest +import numpy as np + +from ash_model import ASH +from ash_model.paths import time_respecting_random_walks, TemporalEdge + + +class TimeRespectingRandomWalksCase(unittest.TestCase): + @staticmethod + def get_hypergraph(): + a = ASH() + # same structure used in test_time_respecting_walks + a.add_hyperedge([1, 2, 3], 0, 4) # e1: t in [0,3] + a.add_hyperedge([1, 4], 0, 1) # e2: t in [0,0] + a.add_hyperedge([1, 2, 3, 4], 2, 3) # e3: t in [2] + a.add_hyperedge([1, 3, 4], 2, 3) # e4: t in [2] + a.add_hyperedge([3, 4], 3, 4) # e5: t in [3] + return a + + @staticmethod + def get_larger_hypergraph(): + """ + Build a more complex temporal hypergraph for stress testing. + - 10 timestamps (0-9) + - 8 nodes (1-8) + - 15 hyperedges with overlapping temporal windows + - Multiple paths of varying lengths and complexities + """ + h = ASH() + # Early period connections (t=0-2) + h.add_hyperedge([1, 2, 3], 0, 2) # e1 + h.add_hyperedge([2, 3, 4], 0, 3) # e2 + h.add_hyperedge([1, 4, 5], 1, 3) # e3 + + # Middle period - denser connectivity (t=2-5) + h.add_hyperedge([3, 4, 5, 6], 2, 5) # e4 + h.add_hyperedge([4, 5, 6], 3, 6) # e5 + h.add_hyperedge([1, 2, 6, 7], 3, 5) # e6 + h.add_hyperedge([5, 6, 7], 4, 7) # e7 + + # Late period connections (t=5-9) + h.add_hyperedge([6, 7, 8], 5, 8) # e8 + h.add_hyperedge([7, 8], 6, 9) # e9 + h.add_hyperedge([1, 8], 7, 9) # e10 + + # Additional cross-temporal bridges + h.add_hyperedge([2, 5, 8], 4, 8) # e11 + h.add_hyperedge([3, 6], 3, 7) # e12 + h.add_hyperedge([1, 3, 7], 5, 8) # e13 + h.add_hyperedge([4, 7, 8], 6, 9) # e14 + h.add_hyperedge([2, 4, 6, 8], 5, 9) # e15 + + return h + + def test_node_random_walks_time_respecting(self): + a = self.get_hypergraph() + # walks on nodes, s=1. Ensure walks are time-respecting (forward in time only) + walks = time_respecting_random_walks( + a, + s=1, + start_from=None, # let it pick active nodes at first timestamps + stop_at=None, + start=0, + end=4, # Extended to t=4 to allow more transitions + num_walks=20, # Increased to improve chances of generating walks + walk_length=5, + edge=False, + p=1.0, + q=1.0, + threads=-1, + ) + # Expect at least one walk + self.assertTrue(len(walks) > 0) + + # Note: Node walks are returned as arrays without explicit timestamps, + # but they should still follow the time-respecting DAG structure. + # The validation happens in the DAG construction (temporal_s_dag) + # where only forward-in-time edges are created. + + # Walks always stop at temporal sinks (nodes with no forward neighbors) + walks_stop = time_respecting_random_walks( + a, + s=1, + start_from=None, + stop_at=None, + start=0, + end=4, + num_walks=10, + walk_length=5, + edge=False, + ) + self.assertTrue(len(walks_stop) > 0) + for w in walks_stop: + # Walks should not exceed the requested length + self.assertTrue(len(w) <= 5) + + def test_edge_random_walks_time_respecting(self): + a = self.get_hypergraph() + # walks on hyperedges; verify time-respecting (strictly increasing timestamps) + walks_map = time_respecting_random_walks( + a, + s=1, + start_from="e1", + stop_at=None, + start=0, + end=4, # Extended to t=4 to allow more transitions + num_walks=10, # Increased for better chance of generating walks + walk_length=4, + edge=True, + p=1.0, + q=1.0, + threads=-1, + ) + # Flatten and check + all_paths = [p for paths in walks_map.values() for p in paths] + self.assertTrue(len(all_paths) > 0) + + # Verify time-respecting property: each consecutive TemporalEdge must have strictly later timestamp + for p in all_paths: + for i, (e1, e2) in enumerate(zip(p, p[1:])): + self.assertIsInstance(e1, TemporalEdge) + self.assertIsInstance(e2, TemporalEdge) + # Time-respecting: next edge must occur at a strictly later timestamp + self.assertGreater( + e2.tid, + e1.tid, + msg=f"Step {i}: {e1} -> {e2} violates time-respecting property (tid should increase)", + ) + + # Walks always stop at temporal sinks (edges with no forward s-incident neighbors) + walks_map_stop = time_respecting_random_walks( + a, + s=1, + start_from="e1", + stop_at=None, + start=0, + end=4, + num_walks=5, + walk_length=4, + edge=True, + ) + all_paths_stop = [p for paths in walks_map_stop.values() for p in paths] + # Verify all paths respect time ordering + for p in all_paths_stop: + for e1, e2 in zip(p, p[1:]): + self.assertGreater(e2.tid, e1.tid, msg=f"Invalid step: {e1} -> {e2}") + + def test_larger_network_node_walks(self): + """Test time-respecting random walks on a larger temporal network with 10 timestamps.""" + h = self.get_larger_hypergraph() + + # Generate node walks across the full temporal range + walks = time_respecting_random_walks( + h, + s=1, + start_from=None, + stop_at=None, + start=0, + end=9, + num_walks=50, + walk_length=8, + edge=False, + p=1.0, + q=1.0, + threads=-1, + ) + + # Should generate walks given the dense connectivity + self.assertGreater(len(walks), 0, "Should generate walks on larger network") + + # Verify walks stay within expected node range + for w in walks: + for node in w: + node_id = int(str(node)) + self.assertIn( + node_id, range(1, 9), f"Node {node_id} out of expected range" + ) + + def test_larger_network_edge_walks_long_paths(self): + """Test that longer paths can be generated in a larger temporal network.""" + h = self.get_larger_hypergraph() + + # Try to generate longer walks (up to 10 steps) + walks_map = time_respecting_random_walks( + h, + s=1, + start_from="e1", # Start from early hyperedge + stop_at=None, + start=0, + end=9, + num_walks=30, + walk_length=10, + edge=True, + p=1.0, + q=1.0, + threads=-1, + ) + + all_paths = [p for paths in walks_map.values() for p in paths] + self.assertGreater( + len(all_paths), 0, "Should generate edge walks on larger network" + ) + + # Check that we can get some longer walks (>= 5 steps) + longer_walks = [p for p in all_paths if len(p) >= 5] + self.assertGreater( + len(longer_walks), 0, "Should generate some longer walks in dense network" + ) + + # Verify all walks maintain time-respecting property + for p in all_paths: + timestamps = [e.tid for e in p] + self.assertEqual( + timestamps, + sorted(timestamps), + msg=f"Walk timestamps not strictly increasing: {timestamps}", + ) + # Check strict increase (no equal consecutive timestamps) + for i in range(len(timestamps) - 1): + self.assertLess(timestamps[i], timestamps[i + 1]) + + def test_larger_network_temporal_span_coverage(self): + """Test that walks can span across significant temporal ranges.""" + h = self.get_larger_hypergraph() + + # Generate edge walks + walks_map = time_respecting_random_walks( + h, + s=1, + start_from=None, + stop_at=None, + start=0, + end=9, + num_walks=100, + walk_length=12, + edge=True, + p=1.0, + q=1.0, + threads=-1, + ) + + all_paths = [p for paths in walks_map.values() for p in paths] + + # Calculate temporal span for each walk (last_timestamp - first_timestamp) + temporal_spans = [] + for p in all_paths: + if len(p) > 0: + span = p[-1].tid - p[0].tid + temporal_spans.append(span) + + # Should have at least one walk spanning multiple timestamps + self.assertGreater(len(temporal_spans), 0) + max_span = max(temporal_spans) + self.assertGreater( + max_span, 2, "Should generate walks spanning more than 2 timestamps" + ) + + # Check that we have diversity in temporal spans + unique_spans = set(temporal_spans) + self.assertGreater( + len(unique_spans), 1, "Should have walks with varying temporal spans" + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/paths/test_time_respecting_walks.py b/ash_model/test/paths/test_time_respecting_walks.py new file mode 100644 index 0000000..4d85c7a --- /dev/null +++ b/ash_model/test/paths/test_time_respecting_walks.py @@ -0,0 +1,168 @@ +import unittest + +from ash_model import ASH +from ash_model.paths import ( + all_time_respecting_s_walks, + annotate_walks, + temporal_s_dag, + time_respecting_s_walks, +) + + +class TimeRespectingWalksCase(unittest.TestCase): + @staticmethod + def get_hypergraph(): + a = ASH() + a.add_hyperedge([1, 2, 3], 0, 4) + a.add_hyperedge([1, 4], 0, 1) + a.add_hyperedge([1, 2, 3, 4], 2, 3) + a.add_hyperedge([1, 3, 4], 2, 3) + a.add_hyperedge([3, 4], 3, 4) + return a + + def test_incidence(self): + a = self.get_hypergraph() + self.assertEqual( + sorted(a.get_s_incident("e1", s=1, start=1, end=1)), [("e2", 1)] + ) + self.assertEqual( + sorted(a.get_s_incident("e1", s=1, start=2, end=2)), [("e3", 3), ("e4", 2)] + ) + self.assertEqual( + sorted(a.get_s_incident("e1", s=1, start=0, end=2)), + [("e2", 1), ("e3", 3), ("e4", 2)], + ) + + def test_temporal_dag(self): + a = self.get_hypergraph() + dg, sources, targets = temporal_s_dag(a, s=2, start_from="e1", edge=True) + + # e1 can start time-respecting walks from t0, t1, and t2 (has s-incident neighbors in future) + self.assertEqual(len(sources), 3) + # Can reach e3 and e4 at t2 and t3, plus e5 at t3 and t4 + self.assertEqual(len(targets), 6) + + dg, sources, targets = temporal_s_dag( + a, s=1, start_from="e1", start=0, end=1, edge=True + ) + # In time window [0,1], e1 can only start from t0 (reaching e2 at t1) + self.assertEqual(len(sources), 1) + # Only e2_1 is reachable + self.assertEqual(len(targets), 1) + + def test_time_respecting_s_walks(self): + a = self.get_hypergraph() + pts = time_respecting_s_walks(a, 1, start_from="e1", stop_at="e5") + + for p in pts: + self.assertIsInstance(p, tuple) + + # When start=4 and end=4, there's only one timestamp, so no future timestamps + # exist for time-respecting walks. This correctly returns 0 walks. + self.assertEqual( + len( + time_respecting_s_walks( + a, 1, start_from="e1", stop_at="e5", start=4, end=4 + ) + ), + 0, + ) + + pts = time_respecting_s_walks(a, 1, start_from="e1", stop_at="e5", sample=0.5) + for p in pts: + self.assertIsInstance(p, tuple) + + def test_all_time_respecting_paths(self): + a = self.get_hypergraph() + pts = all_time_respecting_s_walks(a, s=1) + + for p in pts: + self.assertIsInstance(p, tuple) + + def test_annotated_paths(self): + a = self.get_hypergraph() + pts = all_time_respecting_s_walks(a, s=1) + + for _, ap in pts.items(): + v = annotate_walks(ap) + for k, i in v.items(): + self.assertIn( + k, + [ + "shortest", + "fastest", + "foremost", + "heaviest", + "fastest_shortest", + "fastest_heaviest", + "shortest_fastest", + "shortest_heaviest", + "heaviest_shortest", + "heaviest_fastest", + ], + ) + self.assertIsInstance(i, list) + + def test_complex_temporal_network(self): + """Test time-respecting walks on a more complex temporal network.""" + h = ASH() + # Build a network with 12 timestamps and more complex structure + # Early phase (t=0-3) + h.add_hyperedge([1, 2, 3], 0, 2) # e1 + h.add_hyperedge([2, 3, 4], 1, 3) # e2 + h.add_hyperedge([3, 4, 5], 2, 4) # e3 + + # Middle phase (t=4-7) - denser connections + h.add_hyperedge([1, 4, 6], 4, 6) # e4 + h.add_hyperedge([2, 5, 6], 4, 7) # e5 + h.add_hyperedge([3, 5, 7], 5, 8) # e6 + h.add_hyperedge([4, 6, 7], 6, 9) # e7 + + # Late phase (t=8-11) + h.add_hyperedge([5, 7, 8], 8, 10) # e8 + h.add_hyperedge([6, 7, 8], 9, 11) # e9 + + # Cross-phase bridges + h.add_hyperedge([1, 5, 8], 5, 10) # e10 + h.add_hyperedge([2, 6], 3, 9) # e11 + + # Test DAG construction with multiple sources + dg, sources, targets = temporal_s_dag( + h, s=1, start_from=["e1", "e2"], edge=True + ) + + self.assertGreater(len(sources), 0, "Should have sources") + self.assertGreater(len(targets), 0, "Should have targets") + self.assertGreater(dg.number_of_edges(), 0, "Should have edges in DAG") + + # Test walks enumeration from early to late network + walks = time_respecting_s_walks( + h, s=1, start_from="e1", stop_at=None, start=0, end=11 + ) + + # Should generate walks across temporal range + self.assertGreater(len(walks), 0, "Should generate walks in complex network") + + # Verify temporal properties of generated walks + all_walks = [w for walk_list in walks.values() for w in walk_list] + + # Check for walks with good temporal span + temporal_spans = [w[-1].tid - w[0].tid for w in all_walks if len(w) > 0] + if temporal_spans: + max_span = max(temporal_spans) + self.assertGreater( + max_span, 3, "Should have walks spanning multiple timestamps" + ) + + # Verify strict temporal ordering in all walks + for walk in all_walks: + timestamps = [e.tid for e in walk] + self.assertEqual( + timestamps, + sorted(timestamps), + msg=f"Walk does not have strictly increasing timestamps: {timestamps}", + ) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/test_ash.py b/ash_model/test/test_ash.py deleted file mode 100644 index 2f8fe48..0000000 --- a/ash_model/test/test_ash.py +++ /dev/null @@ -1,445 +0,0 @@ -import json -import unittest - -from networkx.algorithms import bipartite - -from ash_model import ASH, NProfile - - -class ASHTestCase(unittest.TestCase): - def test_add_node(self): - a = ASH(hedge_removal=True) - a.add_node(1, start=0, end=2, attr_dict={"label": "A"}) - self.assertEqual(a.has_node(1), True) - - a.add_node(2, start=4, end=10, attr_dict=NProfile(2, name="Giulio")) - self.assertEqual(a.has_node(2), True) - - def test_add_nodes(self): - a = ASH(hedge_removal=True) - a.add_nodes( - [1, 2], - start=0, - end=2, - node_attr_dict={1: {"label": "A"}, 2: {"label": "B"}}, - ) - self.assertEqual(a.has_node(1), True) - self.assertEqual(a.has_node(2), True) - self.assertEqual(a.has_node(1, tid=0), True) - self.assertEqual(a.has_node(1, tid=3), False) - self.assertEqual(a.has_node(1, tid=2), True) - self.assertEqual(a.avg_number_of_nodes(), 2) - - self.assertEqual(a.get_node_presence(1), [0, 1, 2]) - - self.assertEqual(a.coverage(), 1) - self.assertEqual(a.node_contribution(1), 1) - - def test_degree_dist(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([15, 25], 0) - a.add_hyperedge([1, 24, 34], 0) - a.add_hyperedge([1, 2, 5, 6], 0) - a.add_hyperedge([1, 2, 5], 1) - a.add_hyperedge([3, 4, 5, 10], 1) - a.add_hyperedge([3, 4, 5, 12], 1) - - self.assertDictEqual(a.node_degree_distribution(), {4: 2, 3: 2, 1: 7, 2: 1}) - self.assertDictEqual( - a.node_degree_distribution(start=0), {1: 7, 0: 3, 3: 1, 2: 1} - ) - self.assertDictEqual( - a.node_degree_distribution(start=0, end=1), {4: 2, 3: 2, 1: 7, 2: 1} - ) - - def test_node_attributes(self): - a = ASH(hedge_removal=True) - a.add_node(1, start=0, end=2, attr_dict={"label": "A"}) - - attr = a.get_node_profile(1) - self.assertEqual( - attr, NProfile(1, **{"t": [[0, 2]], "label": {0: "A", 1: "A", 2: "A"}}) - ) - attr = a.get_node_profile(1, tid=0) - self.assertEqual(attr, NProfile(1, **{"label": "A"})) - - label = a.get_node_attribute(1, attr_name="label") - self.assertEqual(label, {0: "A", 1: "A", 2: "A"}) - - label = a.get_node_attribute(1, attr_name="label", tid=0) - self.assertEqual(label, "A") - - def test_node_attributes_to_attribute_values(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 3, 4], 1) - a.add_hyperedge([3, 4], 1) - - a.add_node( - 1, - start=0, - end=0, - attr_dict=NProfile(node_id=1, party="L", age=37, gender="M"), - ) - a.add_node( - 1, - start=1, - end=1, - attr_dict=NProfile(node_id=1, party="R", age=37, gender="M"), - ) - a.add_node( - 2, - start=0, - end=0, - attr_dict=NProfile(node_id=2, party="L", age=20, gender="F"), - ) - a.add_node( - 3, - start=0, - end=1, - attr_dict=NProfile(node_id=3, party="L", age=11, gender="F"), - ) - a.add_node( - 4, - start=0, - end=1, - attr_dict=NProfile(node_id=4, party="R", age=45, gender="M"), - ) - - res = a.node_attributes_to_attribute_values() - self.assertDictEqual( - res, {"party": {"L", "R"}, "age": {11, 20, 37, 45}, "gender": {"F", "M"}} - ) - - res = a.node_attributes_to_attribute_values(categorical=True) - self.assertDictEqual(res, {"party": {"L", "R"}, "gender": {"F", "M"}}) - - for tid in a.temporal_snapshots_ids(): - res = a.node_attributes_to_attribute_values(tid=tid) - self.assertIsInstance(res, dict) - - def test_node_profiles(self): - a = ASH(hedge_removal=True) - a.add_node(1, start=0, end=2, attr_dict=NProfile(1, label="A")) - - attr = a.get_node_profile(1) - self.assertEqual( - attr, NProfile(1, **{"t": [[0, 2]], "label": {0: "A", 1: "A", 2: "A"}}) - ) - attr = a.get_node_profile(1, tid=0) - self.assertEqual(attr, NProfile(1, **{"label": "A"})) - - label = a.get_node_attribute(1, attr_name="label") - self.assertEqual(label, {0: "A", 1: "A", 2: "A"}) - - label = a.get_node_attribute(1, attr_name="label", tid=0) - self.assertEqual(label, "A") - - a.add_node(1, start=3, end=4, attr_dict=NProfile(1, label="B")) - attr = a.get_node_profile(1, 3) - self.assertEqual(attr, NProfile(1, **{"label": "B"})) - - def test_node_set(self): - a = ASH(hedge_removal=True) - a.add_node(1, start=0, end=0, attr_dict={"label": "A"}) - a.add_node(2, start=1, end=3, attr_dict={"label": "A"}) - a.add_node(3, start=3, end=4, attr_dict={"label": "A"}) - - self.assertEqual(a.get_node_set(), {1, 2, 3}) - self.assertEqual(a.get_node_set(tid=0), {1}) - self.assertEqual(a.get_node_set(tid=3), {2, 3}) - self.assertEqual(a.get_node_set(tid=4), {3}) - - self.assertEqual(a.get_number_of_nodes(), 3) - self.assertEqual(a.get_number_of_nodes(0), 1) - - def test_node_iterator(self): - a = ASH(hedge_removal=True) - a.add_node(1, start=0, end=0, attr_dict={"label": "A"}) - a.add_node(2, start=1, end=3, attr_dict={"label": "A"}) - a.add_node(3, start=3, end=4, attr_dict={"label": "A"}) - - iter_res = a.node_iterator() - self.assertEqual(list(iter_res), [1, 2, 3]) - - iter_res = a.node_iterator(tid=3) - self.assertEqual(list(iter_res), [2, 3]) - iter_res = a.node_iterator(tid=4) - self.assertEqual(list(iter_res), [3]) - - def test_hyperedge(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0, 1) - a.add_hyperedge([1, 2, 3], 6, 9) - a.add_hyperedge([1, 2, 3], -3, -2) - a.add_hyperedge([3, 4, 5], 3, 4) - - self.assertEqual(a.get_avg_number_of_hyperedges(), 1.0) - self.assertEqual(a.hyperedge_contribution("e1"), 0.8) - - self.assertEqual(a.has_hyperedge([1, 2, 3]), True) - self.assertEqual(a.has_hyperedge([1, 2, 4]), False) - self.assertEqual(a.has_hyperedge([1, 2, 3], tid=0), True) - self.assertEqual(a.has_hyperedge([1, 2, 3], tid=5), False) - - self.assertEqual(a.get_size(), 2) - self.assertEqual(a.get_size(0), 1) - - self.assertEqual(a.get_number_of_neighbors(1), 3) - self.assertEqual(a.get_number_of_neighbors(1, hyperedge_size=3), 3) - self.assertEqual(a.get_number_of_neighbors(1, hyperedge_size=4), 0) - self.assertEqual(a.get_number_of_neighbors(1, tid=0), 3) - self.assertEqual(a.get_number_of_neighbors(1, tid=100), 0) - - self.assertEqual(a.get_degree(1), 1) - self.assertEqual(a.get_degree(1, hyperedge_size=3), 1) - self.assertEqual(a.get_degree(1, hyperedge_size=4), 0) - self.assertEqual(a.get_degree(1, tid=0), 1) - self.assertEqual(a.get_degree(1, tid=100), 0) - - hs = a.get_hyperedge_id_set() - self.assertEqual(len(hs), 2) - self.assertEqual(hs, {"e1", "e2"}) - hs = a.get_hyperedge_id_set(tid=4) - self.assertEqual(hs, {"e2"}) - - hs = a.get_hyperedge_id_set(hyperedge_size=3) - self.assertEqual(hs, {"e1", "e2"}) - hs = a.get_hyperedge_id_set(hyperedge_size=4) - self.assertEqual(hs, set()) - hs = a.get_hyperedge_id_set(hyperedge_size=3, tid=4) - self.assertEqual(hs, {"e2"}) - hs = a.get_hyperedge_id_set(hyperedge_size=2, tid=4) - self.assertEqual(hs, set()) - - a.add_hyperedges([[4, 5], [6, 7], [8, 9, 10]], start=3, end=10) - hs = a.get_hyperedge_id_set() - self.assertEqual(len(hs), 5) - self.assertEqual(hs, {"e1", "e2", "e3", "e4", "e5"}) - - self.assertEqual(a.get_hyperedge_id([1, 2, 3]), "e1") - self.assertEqual(a.get_hyperedge_nodes("e1"), [1, 2, 3]) - - self.assertEqual(a.get_hyperedge_weight("e1"), 3) - a.add_hyperedge([1, 2, 3], 9, 11) - self.assertEqual(a.get_hyperedge_weight("e1"), 4) - - self.assertEqual(a.has_hyperedge([1, 2, 3]), True) - self.assertEqual(a.has_hyperedge([1, 2, 3, 4]), False) - self.assertEqual(a.has_hyperedge([1, 2, 3], tid=0), True) - self.assertEqual(a.has_hyperedge([1, 2, 3], tid=100), False) - - self.assertEqual(a.has_hyperedge_id("e1"), True) - self.assertEqual(a.has_hyperedge_id("e9"), False) - self.assertEqual(a.has_hyperedge_id("e1", tid=0), True) - self.assertEqual(a.has_hyperedge_id("e1", tid=100), False) - - self.assertEqual(a.uniformity(), 0.3157894736842105) - - def test_temporal_slice(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0, 1) - a.add_hyperedge([1, 2, 3], 6, 9) - a.add_hyperedge([1, 2, 5], 5, 10) - a.add_hyperedge([3, 4, 5], 3, 4) - - b, old_to_new = a.hypergraph_temporal_slice(0) - self.assertIsInstance(b, ASH) - self.assertEqual(b.get_node_set(), {1, 2, 3, 4, 5}) - - b, old_to_new = a.hypergraph_temporal_slice(0, 0) - self.assertIsInstance(b, ASH) - self.assertEqual(b.get_node_set(), {1, 2, 3}) - - c, old_to_new = a.hypergraph_temporal_slice(5, 7) - self.assertIsInstance(c, ASH) - self.assertEqual(c.get_node_set(), {1, 2, 3, 5}) - - def test_interactions(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0, 1) - a.add_hyperedge([1, 2, 3], 6, 9) - a.add_hyperedge([1, 2, 5], 5, 10) - a.add_hyperedge([3, 4, 5], 3, 4) - - for he in a.stream_interactions(): - self.assertEqual(len(he), 3) - - def test_size_distribution(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([15, 25], 0) - a.add_hyperedge([1, 24, 34], 0) - a.add_hyperedge([1, 2, 5, 6], 0) - a.add_hyperedge([1, 2, 5], 1) - a.add_hyperedge([3, 4, 5, 10], 1) - a.add_hyperedge([3, 4, 5, 12], 1) - - self.assertDictEqual(a.hyperedge_size_distribution(), {2: 1, 3: 3, 4: 3}) - self.assertDictEqual(a.hyperedge_size_distribution(start=0), {2: 1, 3: 2, 4: 1}) - self.assertDictEqual( - a.hyperedge_size_distribution(start=0, end=1), {2: 1, 3: 3, 4: 3} - ) - - self.assertEqual(a.get_degree_by_hyperedge_size(1), {3: 3, 4: 1}) - self.assertEqual(a.get_degree_by_hyperedge_size(1, tid=1), {3: 1}) - - self.assertEqual(a.get_s_degree(1, 4), 1) - self.assertEqual(a.get_s_degree(1, 4, 0), 1) - - def test_star(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([15, 25], 0) - a.add_hyperedge([1, 24, 34], 0) - a.add_hyperedge([1, 2, 5, 6], 0) - a.add_hyperedge([1, 2, 5], 1) - a.add_hyperedge([3, 4, 5, 10], 1) - a.add_hyperedge([3, 4, 5, 12], 1) - - self.assertEqual(a.get_star(1), {"e1", "e3", "e4", "e5"}) - self.assertEqual(a.get_star(1, tid=0), {"e1", "e3", "e4"}) - self.assertEqual(a.get_star(1, tid=0, hyperedge_size=4), {"e4"}) - - def test_str(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 3, 4], 1) - a.add_hyperedge([3, 4], 1) - - a.add_node(1, start=0, end=1, attr_dict=NProfile(node_id=1, party="L", age=37)) - a.add_node(2, start=0, end=1, attr_dict=NProfile(node_id=2, party="L", age=20)) - a.add_node(3, start=0, end=1, attr_dict=NProfile(node_id=3, party="L", age=11)) - a.add_node(4, start=0, end=1, attr_dict=NProfile(node_id=4, party="R", age=45)) - - res = a.__str__() - obj = json.loads(res) - self.assertEqual(list(obj.keys()), ["nodes", "hedges"]) - - def test_line_graph(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([2, 3, 4], 0) - a.add_hyperedge([1, 3], 1) - a.add_hyperedge([3, 4], 1) - - g = a.s_line_graph() - - eds = sorted( - [ - ("e1", "e2"), - ("e1", "e4"), - ("e1", "e3"), - ("e1", "e5"), - ("e2", "e3"), - ("e2", "e4"), - ("e2", "e5"), - ("e3", "e5"), - ("e4", "e3"), - ("e4", "e5"), - ] - ) - - self.assertListEqual(sorted(list(g.edges())), eds) - - g = a.s_line_graph(start=0, end=0) - - eds = sorted([("e1", "e2"), ("e1", "e3"), ("e2", "e3")]) - res = sorted([tuple(sorted(i)) for i in list(g.edges())]) - - self.assertListEqual(res, eds) - - def test_bipartite(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([2, 3, 4], 0) - a.add_hyperedge([1, 3], 1) - a.add_hyperedge([3, 4], 1) - - g = a.bipartite_projection() - self.assertEqual(bipartite.is_bipartite(g), True) - - g = a.bipartite_projection(start=0, end=0) - self.assertEqual(bipartite.is_bipartite(g), True) - - def test_dual(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([2, 3, 4], 0) - a.add_hyperedge([1, 3], 1) - a.add_hyperedge([3, 4], 1) - - g, _ = a.dual_hypergraph() - self.assertEqual(g.get_number_of_nodes(), 5) - - g, _ = a.dual_hypergraph(start=0, end=0) - self.assertEqual(g.get_number_of_nodes(), 3) - - def test_incidence(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([2, 3, 4], 0) - a.add_hyperedge([1, 3], 1) - a.add_hyperedge([3, 4], 1) - - self.assertEqual(a.incidence(["e1", "e2"]), 1) - self.assertEqual(a.incidence(["e1", "e3"], start=0, end=0), 2) - - def test_adjacency(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([2, 3, 4], 0) - a.add_hyperedge([1, 3], 1) - a.add_hyperedge([3, 4], 1) - - self.assertEqual(a.adjacency([1, 3]), 2) - self.assertEqual(a.adjacency([1, 3], start=0, end=0), 1) - - def test_s_incidente(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([1, 2, 4], 0) - - self.assertEqual(a.get_s_incident("e1", s=1), [("e2", 1), ("e3", 2)]) - self.assertEqual(a.get_s_incident("e1", s=2), [("e3", 2)]) - self.assertEqual(a.get_s_incident("e1", s=3), []) - - def test_hyperedge_id_iterator(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0, 1) - a.add_hyperedge([1, 4], 0, 2) - a.add_hyperedge([1, 2, 4], 2, 3) - - self.assertEqual(sorted(list(a.hyperedge_id_iterator())), ["e1", "e2", "e3"]) - self.assertEqual( - sorted(list(a.hyperedge_id_iterator(start=0))), ["e1", "e2", "e3"] - ) - self.assertEqual(sorted(list(a.hyperedge_id_iterator(start=2))), ["e2", "e3"]) - self.assertEqual(sorted(list(a.hyperedge_id_iterator(start=3))), ["e3"]) - - self.assertEqual(sorted(list(a.hyperedge_id_iterator(start=3, end=3))), ["e3"]) - - def test_hyper_subgraph(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([2, 3, 4], 0) - a.add_hyperedge([1, 3], 1) - a.add_hyperedge([3, 4], 1) - - a.add_node(1, start=0, end=1, attr_dict=NProfile(node_id=1, party="L", age=37)) - a.add_node(1, start=0, end=1, attr_dict=NProfile(node_id=2, party="L", age=20)) - - b, eid_map = a.induced_hypergraph(("e1", "e2")) - self.assertEqual(len(eid_map), 2) diff --git a/ash_model/test/test_attribute_analysis.py b/ash_model/test/test_attribute_analysis.py deleted file mode 100644 index 118de42..0000000 --- a/ash_model/test/test_attribute_analysis.py +++ /dev/null @@ -1,156 +0,0 @@ -import unittest - -from ash_model.measures import * - - -class AttributeAnalysisCase(unittest.TestCase): - @staticmethod - def get_hypergraph(): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 3, 4], 1) - a.add_hyperedge([3, 4], 1) - - a.add_node( - 1, - start=0, - end=0, - attr_dict=NProfile(node_id=1, party="L", age=37, gender="M"), - ) - a.add_node( - 1, - start=1, - end=1, - attr_dict=NProfile(node_id=1, party="R", age=37, gender="M"), - ) - a.add_node( - 2, - start=0, - end=0, - attr_dict=NProfile(node_id=2, party="L", age=20, gender="F"), - ) - a.add_node( - 3, - start=0, - end=1, - attr_dict=NProfile(node_id=3, party="L", age=11, gender="F"), - ) - a.add_node( - 4, - start=0, - end=1, - attr_dict=NProfile(node_id=4, party="R", age=45, gender="M"), - ) - return a - - def test_profiles(self): - a = ASH(hedge_removal=True) - a.add_node(1, start=1, end=5, attr_dict=NProfile(1, party="L", age=37)) - a.add_node(2, start=1, end=5, attr_dict=NProfile(2, party="L", age=20)) - a.add_node(3, start=1, end=5, attr_dict=NProfile(3, party="L", age=11)) - a.add_node(4, start=1, end=5, attr_dict=NProfile(4, party="R", age=45)) - a.add_hyperedge([1, 2, 3, 4], 1, 4) - - self.assertEqual( - hyperedge_aggregate_node_profile(a, "e1", 1).get_attributes(), - {"age": 28.25}, - ) - self.assertEqual( - hyperedge_aggregate_node_profile(a, "e1", 1).get_statistic("age", "std"), - {"std": 13.442005058770064}, - ) - self.assertEqual( - hyperedge_most_frequent_node_attribute_value(a, "e1", "party", 1), {"L": 3} - ) - - def test_hyperedge_profile_purity(self): - a = self.get_hypergraph() - - for tid in a.temporal_snapshots_ids(): - hes = a.get_hyperedge_id_set(tid=tid) - for he in hes: - res = hyperedge_profile_purity(a, he, tid) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - res = average_hyperedge_profile_purity(a, tid=tid, by_label=False) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - res = average_hyperedge_profile_purity(a, tid=tid, by_label=True) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - - def test_hyperedge_profile_entropy(self): - a = self.get_hypergraph() - - for tid in a.temporal_snapshots_ids(): - hes = a.get_hyperedge_id_set(tid=tid) - for he in hes: - res = hyperedge_profile_entropy(a, he, tid) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - res = average_hyperedge_profile_entropy(a, tid) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - - def test_star_profile_homogeneity(self): - a = self.get_hypergraph() - - hom = star_profile_homogeneity(a, node_id=1, tid=0) - self.assertEqual(hom, {"gender": 0.6666666666666666, "party": 1.0}) - for tid in a.temporal_snapshots_ids(): - for method in ["aggregate", "collapse"]: - for n in a.get_node_set(tid=tid): - res = star_profile_homogeneity(a, n, tid, method) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - - res = average_star_profile_homogeneity( - a, tid=tid, method=method, by_label=False - ) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - res = average_star_profile_homogeneity( - a, tid=tid, method=method, by_label=True - ) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - - def test_star_profile_entropy(self): - a = self.get_hypergraph() - - ent = star_profile_entropy(a, node_id=1, tid=0) - self.assertEqual(ent, {"party": 0, "gender": 0.9182958340544896}) - for tid in a.temporal_snapshots_ids(): - nodes = a.get_node_set(tid=tid) - for method in ["aggregate", "collapse"]: - for n in nodes: - res = star_profile_entropy(a, n, tid, method) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - res = average_star_profile_entropy(a, tid, method=method) - self.assertListEqual(sorted(list(res.keys())), ["gender", "party"]) - - def test_consistency(self): - a = self.get_hypergraph() - res = consistency(a) - - self.assertIsInstance(res, dict) - self.assertEqual(res[1]["party"], 0) - self.assertEqual(res[1]["gender"], 1) - - def test_average_group_degree(self): - a = self.get_hypergraph() - - res = average_group_degree(a, tid=0) - self.assertDictEqual( - res, - { - "party": {"R": 2.0, "L": 2.3333333333333335}, - "gender": {"M": 2.5, "F": 2.0}, - }, - ) - - res = average_group_degree(a, tid=0, hyperedge_size=2) - self.assertDictEqual( - res, - { - "party": {"R": 1.0, "L": 0.3333333333333333}, - "gender": {"M": 1.0, "F": 0.0}, - }, - ) - for tid in a.temporal_snapshots_ids(): - res = average_group_degree(a, tid=tid) - self.assertIsInstance(res, dict) diff --git a/ash_model/test/test_clustering.py b/ash_model/test/test_clustering.py deleted file mode 100644 index fdacefa..0000000 --- a/ash_model/test/test_clustering.py +++ /dev/null @@ -1,80 +0,0 @@ -import unittest - -from ash_model.measures import * - - -class ClusteringTestCase(unittest.TestCase): - def test_LCC(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2], 0) - a.add_hyperedge([1, 3], 0) - a.add_hyperedge([1, 4], 0) - - LCC = s_local_clustering_coefficient(a, 1, "e1") - self.assertEqual(LCC, 0) - - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3, 5], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 2, 3, 4, 5], 0) - - LCC = s_local_clustering_coefficient(a, 1, "e1") - self.assertEqual(LCC, 0) - - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 6, 7], 0) - a.add_hyperedge([1, 2, 3, 4, 5], 0) - a.add_hyperedge([3, 4, 5, 6, 7], 0) - - LCC = s_local_clustering_coefficient(a, 1, "e1") - self.assertEqual(LCC, 1) - - def test_avg_LCC(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2], 0) - a.add_hyperedge([1, 3], 0) - a.add_hyperedge([1, 4], 0) - - LCC = average_s_local_clustering_coefficient(a, 1) - self.assertEqual(LCC, 0) - - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3, 5], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 2, 3, 4, 5], 0) - - LCC = average_s_local_clustering_coefficient(a, 1) - self.assertEqual(LCC, 0) - - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 6, 7], 0) - a.add_hyperedge([1, 2, 3, 4, 5], 0) - a.add_hyperedge([3, 4, 5, 6, 7], 0) - - LCC = average_s_local_clustering_coefficient(a, 1) - self.assertEqual(LCC, 1) - - def test_s_intersections(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2], 0) - a.add_hyperedge([1, 3], 0) - a.add_hyperedge([1, 4], 0) - - res = s_intersections(a, 1) - self.assertEqual(res, 3) - - def test_inclusiveness(self): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2], 0) - a.add_hyperedge([1, 3], 0) - a.add_hyperedge([1, 4], 0) - res = inclusiveness(a) - self.assertEqual(res, 0) - a.add_hyperedge([1, 2, 3, 5], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - res = inclusiveness(a) - self.assertEqual(res, 0.6) - a.add_hyperedge([1, 2, 3, 4, 5], 0) - a.add_hyperedge([3, 4, 5, 6, 7], 0) - res = inclusiveness(a) - self.assertEqual(res, 0.7142857142857143) diff --git a/ash_model/test/test_io.py b/ash_model/test/test_io.py deleted file mode 100644 index 29fa715..0000000 --- a/ash_model/test/test_io.py +++ /dev/null @@ -1,103 +0,0 @@ -import unittest -from ash_model import ASH, NProfile -from ash_model.readwrite import * -import os - - -class IOTestCase(unittest.TestCase): - @staticmethod - def get_hypergraph(): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 3, 4], 1) - a.add_hyperedge([3, 4], 1) - - a.add_node(1, start=0, end=0, attr_dict=NProfile(node_id=1, party="L", age=37)) - a.add_node(1, start=1, end=1, attr_dict=NProfile(node_id=1, party="R", age=37)) - a.add_node(2, start=0, end=0, attr_dict=NProfile(node_id=2, party="L", age=20)) - a.add_node(3, start=0, end=1, attr_dict=NProfile(node_id=3, party="L", age=11)) - a.add_node(4, start=0, end=1, attr_dict=NProfile(node_id=4, party="R", age=45)) - return a - - def test_read_write_profile_csv(self): - a = self.get_hypergraph() - - write_profiles_to_csv(a, "test_profiles.csv") - res = read_profiles_from_csv("test_profiles.csv") - - for k, v in res.items(): - self.assertEqual(a.has_node(k), True) - for t, p in v.items(): - self.assertEqual(a.has_node(k, t), True) - profile = a.get_node_profile(k, t) - self.assertEqual(a.get_node_profile(k, t) == profile, True) - os.remove("test_profiles.csv") - - def test_read_write_profile_json(self): - a = self.get_hypergraph() - - write_profiles_to_jsonl(a, "test_profiles.json") - res = read_profiles_from_jsonl("test_profiles.json") - - for k, v in res.items(): - self.assertEqual(a.has_node(k), True) - for t, p in v.items(): - self.assertEqual(a.has_node(k, t), True) - profile = a.get_node_profile(k, t) - self.assertEqual(a.get_node_profile(k, t) == profile, True) - - os.remove("test_profiles.json") - - def test_read_write_sh_csv(self): - a = self.get_hypergraph() - - write_sh_to_csv(a, "test_sh.csv") - b = read_sh_from_csv("test_sh.csv") - - self.assertEqual(a.get_hyperedge_id_set(), b.get_hyperedge_id_set()) - self.assertEqual( - sorted(list(a.node_iterator())), sorted(list(b.node_iterator())) - ) - self.assertEqual( - sorted(a.temporal_snapshots_ids()), sorted(b.temporal_snapshots_ids()) - ) - for tid in a.temporal_snapshots_ids(): - self.assertEqual( - len(a.get_hyperedge_id_set(tid)), len(b.get_hyperedge_id_set(tid)) - ) - self.assertEqual( - len(list(a.node_iterator(tid))), len(list(b.node_iterator(tid))) - ) - - os.remove("test_sh.csv") - - def test_read_write_ash(self): - a = self.get_hypergraph() - write_ash_to_json(a, "test_ash.json") - b = read_ash_from_json("test_ash.json") - - self.assertEqual(a.get_hyperedge_id_set(), b.get_hyperedge_id_set()) - self.assertEqual( - sorted(list(a.node_iterator())), sorted(list(b.node_iterator())) - ) - self.assertEqual( - sorted(a.temporal_snapshots_ids()), sorted(b.temporal_snapshots_ids()) - ) - for tid in a.temporal_snapshots_ids(): - self.assertEqual( - len(a.get_hyperedge_id_set(tid)), len(b.get_hyperedge_id_set(tid)) - ) - self.assertEqual( - len(list(a.node_iterator(tid))), len(list(b.node_iterator(tid))) - ) - - for node in a.node_iterator(): - tids = a.get_node_presence(node) - for tid in tids: - p1 = a.get_node_profile(node, tid) - p2 = b.get_node_profile(node, tid) - self.assertEqual(p1 == p2, True) - - os.remove("test_ash.json") diff --git a/ash_model/test/test_models.py b/ash_model/test/test_models.py deleted file mode 100644 index f95d865..0000000 --- a/ash_model/test/test_models.py +++ /dev/null @@ -1,35 +0,0 @@ -import unittest - -from ash_model.models import * - - -class ModelsTestCase(unittest.TestCase): - def test_random_ASH(self): - a = random_ASH( - n_nodes=100, - n_hyperedges=100, - max_edge_size=10, - n_tids=3, - attr_to_vals_dict={"party": ["L", "R"], "age": [20, 30, 40]}, - ) - - self.assertEqual(a.get_number_of_nodes(), 100) - self.assertEqual(a.get_size(), 100 * 3) - for tid in a.temporal_snapshots_ids(): - self.assertEqual(a.get_size(tid), 100) - self.assertListEqual( - [ - he - for he in a.get_hyperedge_id_set() - if len(a.get_hyperedge_nodes(he)) > 10 - ], - [], - ) - self.assertEqual(len(a.temporal_snapshots_ids()), 3) - - for tid in a.temporal_snapshots_ids(): - for n in a.get_node_set(tid=tid): - attr = a.get_node_attribute(n, "party", tid=tid) - self.assertIn(attr, ["L", "R"]) - attr = a.get_node_attribute(n, "age", tid=tid) - self.assertIn(attr, [20, 30, 40]) diff --git a/ash_model/test/test_s_centralities.py b/ash_model/test/test_s_centralities.py deleted file mode 100644 index 8edc02e..0000000 --- a/ash_model/test/test_s_centralities.py +++ /dev/null @@ -1,141 +0,0 @@ -import unittest -from ash_model import ASH -from ash_model.measures import * - - -class SCentralitiesCase(unittest.TestCase): - @staticmethod - def get_hypergraph(): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 3, 4], 1) - a.add_hyperedge([3, 4], 1) - return a - - def test_centralities(self): - a = self.get_hypergraph() - _almost_equal( - s_betweenness_centrality(a, s=1), - {"e1": 0.0, "e2": 0.0, "e3": 0.0, "e4": 0.0, "e5": 0.0}, - ) - _almost_equal( - s_betweenness_centrality(a, s=1, edges=False), - {1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}, - ) - - _almost_equal( - s_closeness_centrality(a, s=1), - {"e1": 1.0, "e2": 1.0, "e3": 1.0, "e4": 1.0, "e5": 1.0}, - ) - _almost_equal( - s_closeness_centrality(a, s=1, edges=False), - {1: 1.0, 2: 1.0, 3: 1.0, 4: 1.0}, - ) - - _almost_equal( - s_eccentricity(a, s=1), - {"e1": 1.0, "e2": 1.0, "e3": 1.0, "e4": 1.0, "e5": 1.0}, - ) - _almost_equal( - s_eccentricity(a, s=1, edges=False), {1: 1, 2: 1, 3: 1, 4: 1} - ) - - _almost_equal( - s_harmonic_centrality(a, s=1), - {"e1": 4.0, "e3": 4.0, "e5": 4.0, "e4": 4.0, "e2": 4.0}, - ) - _almost_equal( - s_harmonic_centrality(a, s=1, edges=False), {1: 3.0, 2: 3.0, 3: 3.0, 4: 3.0} - ) - - _almost_equal( - s_katz(a, s=1), - { - "e1": 0.447213595499958, - "e2": 0.4472135954999579, - "e3": 0.447213595499958, - "e4": 0.4472135954999579, - "e5": 0.4472135954999579, - }, - ) - _almost_equal( - s_katz(a, s=1, edges=False), - {1: 0.49999999999999983, 2: 0.5, 3: 0.5, 4: 0.49999999999999994}, - ) - - _almost_equal( - s_load_centrality(a, s=1), - {"e1": 0.0, "e2": 0.0, "e3": 0.0, "e4": 0.0, "e5": 0.0}, - ) - _almost_equal( - s_load_centrality(a, s=1, edges=False), {1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0} - ) - - _almost_equal( - s_eigenvector_centrality(a, s=1), - { - "e1": 0.447213595499958, - "e2": 0.447213595499958, - "e3": 0.447213595499958, - "e4": 0.44721359549995787, - "e5": 0.4472135954999579, - }, - ) - _almost_equal( - s_eigenvector_centrality(a, s=1, edges=False), - { - 1: 0.4999999999999999, - 2: 0.5000000000000002, - 3: 0.4999999999999999, - 4: 0.5, - }, - ) - - _almost_equal( - s_information_centrality(a, s=1), - {"e1": 0.625, "e2": 0.625, "e3": 0.625, "e4": 0.625, "e5": 0.625}, - ) - _almost_equal( - s_information_centrality(a, s=1, edges=False), - { - 1: 0.6666666666666666, - 2: 0.6666666666666666, - 3: 0.6666666666666666, - 4: 0.6666666666666666, - }, - ) - - _almost_equal( - s_second_order_centrality(a, s=1), - { - "e1": 3.4641016151377535, - "e2": 3.4641016151377544, - "e3": 3.4641016151377535, - "e4": 3.4641016151377544, - "e5": 3.4641016151377544, - }, - ) - _almost_equal( - s_second_order_centrality(a, s=1, edges=False), - { - 1: 2.4494897427831774, - 2: 2.4494897427831774, - 3: 2.4494897427831774, - 4: 2.4494897427831774, - }, - ) - - _almost_equal(s_second_order_centrality(a, s=1, edges=False), { - 1: 2.4494897427831774, - 2: 2.4494897427831774, - 3: 2.4494897427831774, - 4: 2.4494897427831774, - }) - - -def _almost_equal(A, B): - for k in A: - np.testing.assert_almost_equal(A[k], B[k]) - diff --git a/ash_model/test/test_static_viz.py b/ash_model/test/test_static_viz.py deleted file mode 100644 index 692f7c8..0000000 --- a/ash_model/test/test_static_viz.py +++ /dev/null @@ -1,37 +0,0 @@ -import unittest - -from ash_model.viz import * - - -class StaticVizTestCase(unittest.TestCase): - @staticmethod - def get_hypergraph(): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([15, 25], 0) - a.add_hyperedge([1, 24, 34], 0) - a.add_hyperedge([1, 2, 5, 6], 0) - a.add_hyperedge([1, 2, 5], 1) - a.add_hyperedge([3, 4, 5, 10], 1) - a.add_hyperedge([3, 4, 5, 12], 1) - return a - - def test_plot_s_degrees(self): - a = self.get_hypergraph() - ax = plot_s_degrees(a, smax=3) - self.assertIsInstance(ax, plt.Axes) - - def test_plot_hyperedge_size_distribution(self): - a = self.get_hypergraph() - ax = plot_hyperedge_size_distribution(a) - self.assertIsInstance(ax, plt.Axes) - - def test_plot_degree_distribution(self): - a = self.get_hypergraph() - ax = plot_degree_distribution(a) - self.assertIsInstance(ax, plt.Axes) - - def test_plot_s_ranks(self): - a = self.get_hypergraph() - ax = plot_s_ranks(a, smax=3) - self.assertIsInstance(ax, plt.Axes) diff --git a/ash_model/test/test_temporal_viz.py b/ash_model/test/test_temporal_viz.py deleted file mode 100644 index a4540f3..0000000 --- a/ash_model/test/test_temporal_viz.py +++ /dev/null @@ -1,102 +0,0 @@ -import unittest - -from ash_model.viz import * - - -class TemporalVizTestCase(unittest.TestCase): - @staticmethod - def get_hypergraph(): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([1, 4], 0) - a.add_hyperedge([1, 2, 3, 4], 0) - a.add_hyperedge([1, 3, 4], 1) - a.add_hyperedge([3, 4], 1) - - a.add_node( - 1, - start=0, - end=0, - attr_dict=NProfile(node_id=1, party="L", age=37, gender="M"), - ) - a.add_node( - 1, - start=1, - end=1, - attr_dict=NProfile(node_id=1, party="R", age=37, gender="M"), - ) - a.add_node( - 2, - start=0, - end=0, - attr_dict=NProfile(node_id=2, party="L", age=20, gender="F"), - ) - a.add_node( - 3, - start=0, - end=1, - attr_dict=NProfile(node_id=3, party="L", age=11, gender="F"), - ) - a.add_node( - 4, - start=0, - end=1, - attr_dict=NProfile(node_id=4, party="R", age=45, gender="M"), - ) - return a - - def test_plot_structure_dynamics(self): - a = self.get_hypergraph() - - ax = plot_structure_dynamics( - a, average_s_local_clustering_coefficient, func_params={"s": 2} - ) - self.assertIsInstance(ax, plt.Axes) - ax = plot_structure_dynamics(a, inclusiveness, func_params={}) - self.assertIsInstance(ax, plt.Axes) - - def test_plot_attribute_dynamics(self): - a = self.get_hypergraph() - ax = plot_attribute_dynamics( - a, attr_name="party", func=average_hyperedge_profile_entropy - ) - self.assertIsInstance(ax, plt.Axes) - ax = plot_attribute_dynamics( - a, - attr_name="party", - func=average_hyperedge_profile_purity, - func_params={"by_label": True}, - ) - self.assertIsInstance(ax, plt.Axes) - ax = plot_attribute_dynamics( - a, - attr_name="party", - func=average_hyperedge_profile_purity, - func_params={"by_label": False}, - ) - self.assertIsInstance(ax, plt.Axes) - ax = plot_attribute_dynamics( - a, - attr_name="party", - func=average_star_profile_homogeneity, - func_params={"by_label": True}, - ) - self.assertIsInstance(ax, plt.Axes) - ax = plot_attribute_dynamics( - a, - attr_name="party", - func=average_star_profile_homogeneity, - func_params={"by_label": False}, - ) - self.assertIsInstance(ax, plt.Axes) - - # def test_plot_temporal_attribute_distribution(self): - # a = self.get_hypergraph() - # for attr_name in ['gender', 'party']: - # ax = plot_temporal_attribute_distribution(a, attr_name) - # self.assertIsInstance(ax, plt.Axes) - - def test_plot_consistency(self): - a = self.get_hypergraph() - ax = plot_consistency(a) - self.assertIsInstance(ax, plt.Axes) diff --git a/ash_model/test/test_time_respecting_walks.py b/ash_model/test/test_time_respecting_walks.py deleted file mode 100644 index 0e5576e..0000000 --- a/ash_model/test/test_time_respecting_walks.py +++ /dev/null @@ -1,89 +0,0 @@ -import unittest -from ash_model import ASH -from ash_model.paths import * -import networkx as nx - - -class TimeRespectingWalksCase(unittest.TestCase): - @staticmethod - def get_hypergraph(): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0, 4) - a.add_hyperedge([1, 4], 0, 1) - a.add_hyperedge([1, 2, 3, 4], 2, 3) - a.add_hyperedge([1, 3, 4], 2, 3) - a.add_hyperedge([3, 4], 3, 4) - return a - - def test_incidence(self): - a = self.get_hypergraph() - self.assertEqual( - sorted(a.get_s_incident("e1", s=1, start=1, end=1)), [("e2", 1)] - ) - self.assertEqual( - sorted(a.get_s_incident("e1", s=1, start=2, end=2)), [("e3", 3), ("e4", 2)] - ) - self.assertEqual( - sorted(a.get_s_incident("e1", s=1, start=0, end=2)), - [("e2", 1), ("e3", 3), ("e4", 2)], - ) - - def test_temporal_dag(self): - a = self.get_hypergraph() - dg, sources, targets = temporal_s_dag(a, s=2, hyperedge_from="e1") - - self.assertEqual(len(sources), 2) - self.assertEqual(len(targets), 5) - - dg, sources, targets = temporal_s_dag( - a, s=1, hyperedge_from="e1", start=0, end=1 - ) - self.assertEqual(len(sources), 2) - self.assertEqual(len(targets), 2) - - def test_time_respecting_s_walks(self): - a = self.get_hypergraph() - pts = time_respecting_s_walks(a, 1, "e1", "e5") - - for p in pts: - self.assertIsInstance(p, tuple) - - self.assertEqual( - len(time_respecting_s_walks(a, 1, "e1", "e5", start=4, end=4)), 1 - ) - - pts = time_respecting_s_walks(a, 1, "e1", "e5", sample=0.5) - - for p in pts: - self.assertIsInstance(p, tuple) - - def test_all_time_respecting_paths(self): - a = self.get_hypergraph() - pts = all_time_respecting_s_walks(a, s=1) - - for p in pts: - self.assertIsInstance(p, tuple) - - def test_annotated_paths(self): - a = self.get_hypergraph() - pts = all_time_respecting_s_walks(a, s=1) - - for _, ap in pts.items(): - v = annotate_walks(ap) - for k, i in v.items(): - self.assertIn( - k, - [ - "shortest", - "fastest", - "foremost", - "heaviest", - "fastest_shortest", - "fastest_heaviest", - "shortest_fastest", - "shortest_heaviest", - "heaviest_shortest", - "heaviest_fastest", - ], - ) - self.assertIsInstance(i, list) diff --git a/ash_model/test/test_utils.py b/ash_model/test/test_utils.py deleted file mode 100644 index 4d808db..0000000 --- a/ash_model/test/test_utils.py +++ /dev/null @@ -1,89 +0,0 @@ -import unittest - -import networkx as nx - -from ash_model import ASH -import ash_model.utils as ut - - -class UtilsTestCase(unittest.TestCase): - @staticmethod - def get_hypergraph(): - a = ASH(hedge_removal=True) - a.add_hyperedge([1, 2, 3], 0) - a.add_hyperedge([15, 25], 0) - a.add_hyperedge([1, 24, 34], 0) - a.add_hyperedge([1, 2, 5, 6], 0) - a.add_hyperedge([1, 2, 5], 1) - a.add_hyperedge([3, 4, 5, 10], 1) - a.add_hyperedge([3, 4, 5, 12], 1) - return a - - def test_node_mapping(self): - a = self.get_hypergraph() - index_to_node, node_to_index = ut.get_node_mapping(a) - self.assertIsInstance(node_to_index, dict) - self.assertIsInstance(index_to_node, dict) - - def test_get_hyperedge_id_mapping(self): - a = self.get_hypergraph() - index_to_edge, edge_to_index = ut.get_hyperedge_id_mapping(a) - self.assertIsInstance(index_to_edge, dict) - self.assertIsInstance(edge_to_index, dict) - - def test_get_incidence_matrix(self): - a = self.get_hypergraph() - _, node_to_index = ut.get_node_mapping(a) - _, edge_to_index = ut.get_hyperedge_id_mapping(a) - M = ut.get_incidence_matrix(a, node_to_index, edge_to_index) - self.assertIsInstance(M, dict) - - M = ut.get_incidence_matrix(a, node_to_index, edge_to_index, tid=0) - self.assertIsInstance(M, dict) - - def test_get_hyperedge_weight_matrix(self): - a = self.get_hypergraph() - _, edge_to_index = ut.get_hyperedge_id_mapping(a) - M = ut.get_hyperedge_weight_matrix(a, edge_to_index) - self.assertIsInstance(M, dict) - - M = ut.get_hyperedge_weight_matrix(a, edge_to_index, tid=0) - self.assertIsInstance(M, dict) - - def test_get_vertex_degree_matrix(self): - a = self.get_hypergraph() - M = ut.get_vertex_degree_matrix(a) - self.assertIsInstance(M, dict) - - M = ut.get_vertex_degree_matrix(a, 1) - self.assertIsInstance(M, dict) - - def test_to_graph_decomposition(self): - a = self.get_hypergraph() - - b = ut.to_graph_decomposition(a) - self.assertIsInstance(b, dict) - self.assertEqual(len(b), 2) - - b = ut.to_graph_decomposition(a, 1) - self.assertIsInstance(b, dict) - self.assertEqual(len(b), 1) - - def test_to_networkx_graph(self): - a = self.get_hypergraph() - - b = ut.to_networkx_graph(a) - self.assertIsInstance(b, dict) - self.assertEqual(len(b), 2) - - b = ut.to_networkx_graph(a, 1) - self.assertIsInstance(b, dict) - self.assertEqual(len(b), 1) - - def test_from_networkx_graph(self): - g = nx.karate_club_graph() - a = ut.from_networkx_graph(g, start=1) - self.assertIsInstance(a, ASH) - - a = ut.from_networkx_graph(g, start=1, end=2) - self.assertIsInstance(a, ASH) diff --git a/ash_model/test/unit/__init__.py b/ash_model/test/unit/__init__.py new file mode 100644 index 0000000..4a52b4a --- /dev/null +++ b/ash_model/test/unit/__init__.py @@ -0,0 +1 @@ +"""Unit tests for core ASH components.""" diff --git a/ash_model/test/unit/classes/__init__.py b/ash_model/test/unit/classes/__init__.py new file mode 100644 index 0000000..54ee90e --- /dev/null +++ b/ash_model/test/unit/classes/__init__.py @@ -0,0 +1 @@ +"""Unit tests for ASH class implementations.""" diff --git a/ash_model/test/unit/classes/test_presence_store.py b/ash_model/test/unit/classes/test_presence_store.py new file mode 100644 index 0000000..5007d4d --- /dev/null +++ b/ash_model/test/unit/classes/test_presence_store.py @@ -0,0 +1,256 @@ +import unittest +import time +import random +from ash_model.classes import DensePresenceStore, IntervalPresenceStore, ASH + + +class TestDensePresenceStore(unittest.TestCase): + def setUp(self): + self.store = DensePresenceStore() + + def test_initially_empty(self): + self.assertEqual(list(self.store.keys()), []) + # get should return default when missing + self.assertEqual(self.store.get(5, {"a"}), {"a"}) + + def test_setdefault_and_item(self): + # setdefault should create the key and return a mutable set + snap = self.store.setdefault(10, set()) + self.assertIsInstance(snap, set) + self.assertEqual(list(self.store.keys()), [10]) + # adding to snapshot + snap.add(42) + self.assertIn(42, self.store[10]) + # __getitem__ should return the same underlying set + self.store[10].add(99) + self.assertIn(99, snap) + + def test_contains_and_len(self): + self.store.setdefault(3, set()).add(7) + self.assertIn(3, self.store) + self.assertEqual(len(self.store), 1) + self.assertEqual(list(iter(self.store)), [3]) + + +class TestIntervalPresenceStore(unittest.TestCase): + def setUp(self): + self.store = IntervalPresenceStore() + + def test_initially_empty(self): + self.assertEqual(list(self.store.keys()), []) + # get should return default when missing + self.assertEqual(self.store.get(100, {"x"}), {"x"}) + # __getitem__ on missing t returns empty set + self.assertEqual(self.store[100], set()) + + def test_add_occurrence_via_setdefault(self): + snap = self.store.setdefault(5, set()) + # add element 1 at time=5 + snap.add(1) + self.assertIn(5, self.store.keys()) + # __getitem__ now shows that element + self.assertEqual(self.store[5], {1}) + # adding twice has no duplicate effects + snap.add(1) + self.assertEqual(self.store[5], {1}) + + def test_remove_occurrence_via_setdefault_discard(self): + snap = self.store.setdefault(7, set()) + snap.add(10) + self.assertIn(7, self.store.keys()) + # discard should remove and clean up keys + snap.discard(10) + self.assertEqual(self.store.get(7, set()), set()) + self.assertNotIn(7, self.store.keys()) + + def test_materialise_read_only(self): + # __getitem__ returns a materialised set; mutating it doesn't affect store + snap = self.store.setdefault(2, set()) + snap.add(99) + view = self.store[2] + view.add(123) + # underlying store unchanged by mutating view + self.assertNotIn(123, self.store[2]) + self.assertIn(99, self.store[2]) + + def test_interval_merging(self): + # add element 1 at time=5 + snap5 = self.store.setdefault(5, set()) + snap5.add(1) + # add same element at time=6 (adjacent), should merge interval to (5,6) + snap6 = self.store.setdefault(6, set()) + snap6.add(1) + self.assertEqual(self.store._intervals[1], [(5, 6)]) + + # add element at time=4 (adjacent to start), should extend to (4,6) + snap4 = self.store.setdefault(4, set()) + snap4.add(1) + self.assertEqual(self.store._intervals[1], [(4, 6)]) + + # add element at time=8 (non‐adjacent), should create a separate interval + snap8 = self.store.setdefault(8, set()) + snap8.add(1) + self.assertCountEqual(self.store._intervals[1], [(4, 6), (8, 8)]) + + def test_add_interval_direct(self): + # directly add a span [3,5] for hid=42 + self.store._add_interval(42, 3, 5) + # interval list should reflect exactly one interval + self.assertEqual(self.store._intervals[42], [(3, 5)]) + # keys() should return 3,4,5 + self.assertCountEqual(self.store.keys(), [3, 4, 5]) + # each timepoint should contain hid=42 + for t in (3, 4, 5): + self.assertIn(42, self.store[t]) + + def test_remove_interval_direct(self): + # seed with a bigger interval, then cut out a middle piece + self.store._add_interval(7, 1, 5) + # remove timepoint 3 from hid=7 + self.store._remove_interval(7, 3, 3) + # should split into [1,2] and [4,5] + self.assertCountEqual(self.store._intervals[7], [(1, 2), (4, 5)]) + # keys now are 1,2,4,5 + self.assertCountEqual(self.store.keys(), [1, 2, 4, 5]) + # ensure 3 is gone + self.assertNotIn(3, self.store.keys()) + self.assertEqual(self.store[3], set()) + + +class TestASHBackends(unittest.TestCase): + """ + Compare two ASH instances seeded with the same hyperedges + but using different presence backends (dense vs interval). + """ + + def setUp(self): + # prepare identical hyperedge data: (nodes, start, end) + self.hyperedges = [ + ([1, 2], 1, 3), + ([2, 3], 2, 5), + ([4], 5, 5), + ] + # ASH with dense snapshots + self.ash_dense = ASH(backend="dense") + # ASH with interval snapshots + self.ash_interval = ASH(backend="interval") + # insert same data + for nodes, start, end in self.hyperedges: + self.ash_dense.add_hyperedge(nodes, start, end) + self.ash_interval.add_hyperedge(nodes, start, end) + + def test_snapshot_keys_equal(self): + # snapshot timestamps should match + keys_dense = set(self.ash_dense.temporal_snapshots_ids()) + keys_interval = set(self.ash_interval.temporal_snapshots_ids()) + self.assertEqual(keys_dense, keys_interval) + + def test_hyperedge_presence_times_equal(self): + # for each hyperedge id, compare presence lists + for hid in self.ash_dense._eid2nids: + # dense returns list of times + times_dense = self.ash_dense.hyperedge_presence(hid) + times_int = self.ash_interval.hyperedge_presence(hid) + self.assertEqual(sorted(times_dense), sorted(times_int)) + + def test_hyperedge_presence_intervals_equal(self): + # compare merged intervals + for hid in self.ash_dense._eid2nids: + iv_dense = self.ash_dense.hyperedge_presence(hid, as_intervals=True) + iv_int = self.ash_interval.hyperedge_presence(hid, as_intervals=True) + # sort intervals for comparison + self.assertCountEqual(iv_dense, iv_int) + + def test_edge_attributes_and_nodes(self): + # ensure node sets match per hyperedge + for hid, nodes in self.ash_dense._eid2nids.items(): + self.assertEqual(nodes, self.ash_interval._eid2nids[hid]) + # star sets equal + self.assertEqual( + set(self.ash_dense._stars[hid]), set(self.ash_interval._stars[hid]) + ) + + +""" +class TestASHBenchmark(unittest.TestCase): + + @classmethod + def setUpClass(cls): + # Generate benchmark hyperedges: source node list, start, end + cls.num_edges = 5000 + cls.time_horizon = 100 + cls.max_span = 50 + cls.hyperedges = [] + for i in range(cls.num_edges): + length = random.randint(1, cls.max_span) + start = random.randint(0, cls.time_horizon - length) + end = start + length + # random small hyperedge of size 3 + nodes = random.sample(range(1000), 3) + cls.hyperedges.append((nodes, start, end)) + + # Initialize ASH instances + cls.ash_dense = ASH(backend="dense") + cls.ash_interval = ASH(backend="interval") + + def test_add_hyperedges(self): + # Benchmark add_hyperedge + t0 = time.perf_counter() + for nodes, start, end in self.hyperedges: + self.ash_dense.add_hyperedge(nodes, start, end) + t1 = time.perf_counter() + dense_time = t1 - t0 + + t0 = time.perf_counter() + for nodes, start, end in self.hyperedges: + self.ash_interval.add_hyperedge(nodes, start, end) + t1 = time.perf_counter() + interval_time = t1 - t0 + + # print(f"add_hyperedge: dense={dense_time:.4f}s, interval={interval_time:.4f}s") + + def test_hyperedge_presence(self): + # Ensure hyperedges built first + # Benchmark hyperedge_presence + sample_ids = list(self.ash_dense._eid2nids.keys())[:100] + + t0 = time.perf_counter() + for hid in sample_ids: + _ = self.ash_dense.hyperedge_presence(hid) + _ = self.ash_dense.hyperedge_presence(hid, as_intervals=True) + t1 = time.perf_counter() + dense_time = t1 - t0 + + t0 = time.perf_counter() + for hid in sample_ids: + _ = self.ash_interval.hyperedge_presence(hid) + _ = self.ash_interval.hyperedge_presence(hid, as_intervals=True) + t1 = time.perf_counter() + interval_time = t1 - t0 + + # print( + # f"hyperedge_presence: dense={dense_time:.4f}s, interval={interval_time:.4f}s" + # ) + + def test_remove_hyperedges(self): + # Benchmark removal of half the hyperedges + ids = list(self.ash_dense._eid2nids.keys()) + to_remove = ids[: len(ids) // 2] + + t0 = time.perf_counter() + for hid in to_remove: + self.ash_dense.remove_hyperedge(hid) + t1 = time.perf_counter() + dense_time = t1 - t0 + + t0 = time.perf_counter() + for hid in to_remove: + self.ash_interval.remove_hyperedge(hid) + t1 = time.perf_counter() + interval_time = t1 - t0 + + # print( + # f"remove_hyperedge: dense={dense_time:.4f}s, interval={interval_time:.4f}s" + # ) + +""" diff --git a/ash_model/test/unit/classes/test_presence_store_performance.py b/ash_model/test/unit/classes/test_presence_store_performance.py new file mode 100644 index 0000000..1a04819 --- /dev/null +++ b/ash_model/test/unit/classes/test_presence_store_performance.py @@ -0,0 +1,219 @@ +import time +import unittest + +from ash_model.classes.presence_store import DensePresenceStore, IntervalPresenceStore + + +class PresenceStoreCorrectnessTestCase(unittest.TestCase): + """Verify that optimized IntervalPresenceStore produces identical output to Dense.""" + + def test_materialise_single_interval(self): + dense = DensePresenceStore() + interval = IntervalPresenceStore() + + # Add hyperedge 1 present at times 0-5 + for t in range(6): + dense.setdefault(t, set()).add(1) + interval._add_interval(1, 0, 5) + + for t in range(-1, 7): + self.assertEqual(dense[t], interval[t], f"Mismatch at t={t}") + + def test_materialise_multiple_intervals(self): + dense = DensePresenceStore() + interval = IntervalPresenceStore() + + # Add hyperedge 1: [0-2], [5-7] + for t in [0, 1, 2, 5, 6, 7]: + dense.setdefault(t, set()).add(1) + interval._add_interval(1, 0, 2) + interval._add_interval(1, 5, 7) + + for t in range(-1, 10): + self.assertEqual(dense[t], interval[t], f"Mismatch at t={t}") + + def test_materialise_many_ids(self): + dense = DensePresenceStore() + interval = IntervalPresenceStore() + + # Add 100 hyperedges with different intervals + for hid in range(100): + start = hid * 2 + end = hid * 2 + 10 + for t in range(start, end + 1): + dense.setdefault(t, set()).add(hid) + interval._add_interval(hid, start, end) + + # Check snapshot at various times + for t in [0, 5, 50, 100, 150, 200]: + self.assertEqual(dense[t], interval[t], f"Mismatch at t={t}") + + def test_keys_after_add_interval(self): + dense = DensePresenceStore() + interval = IntervalPresenceStore() + + # Add hyperedge 1: [10-20] + for t in range(10, 21): + dense.setdefault(t, set()).add(1) + interval._add_interval(1, 10, 20) + + self.assertEqual(set(dense.keys()), set(interval.keys())) + + def test_keys_after_remove_interval(self): + dense = DensePresenceStore() + interval = IntervalPresenceStore() + + # Add hid 1: [0-10], then remove [5-7] + for t in range(11): + dense.setdefault(t, set()).add(1) + for t in [5, 6, 7]: + dense[t].discard(1) + # Remove empty snapshots manually + if not dense[t]: + del dense[t] + + interval._add_interval(1, 0, 10) + interval._remove_interval(1, 5, 7) + + self.assertEqual(set(dense.keys()), set(interval.keys())) + + def test_setdefault_add_remove(self): + dense = DensePresenceStore() + interval = IntervalPresenceStore() + + # Add via setdefault (mimics ASH usage) + dense.setdefault(0, set()).add(1) + dense.setdefault(0, set()).add(2) + dense.setdefault(1, set()).add(1) + + interval.setdefault(0, set()).add(1) + interval.setdefault(0, set()).add(2) + interval.setdefault(1, set()).add(1) + + self.assertEqual(dense[0], interval[0]) + self.assertEqual(dense[1], interval[1]) + self.assertEqual(set(dense.keys()), set(interval.keys())) + + # Remove via mutable view + interval.setdefault(0, set()).discard(1) + dense[0].discard(1) + + self.assertEqual(dense[0], interval[0]) + + +class PresenceStorePerformanceTestCase(unittest.TestCase): + """Benchmark optimized IntervalPresenceStore vs DensePresenceStore.""" + + def test_materialise_performance_many_ids(self): + """Measure time to materialise snapshot with many IDs and intervals.""" + interval = IntervalPresenceStore() + n_ids = 1000 + intervals_per_id = 5 + + # Setup: add many intervals + for hid in range(n_ids): + for i in range(intervals_per_id): + start = hid * 100 + i * 20 + end = start + 10 + interval._add_interval(hid, start, end) + + # Benchmark: materialise at various times + times_to_check = [50, 5000, 10000, 50000, 100000] + start_time = time.perf_counter() + for t in times_to_check: + snapshot = interval[t] + elapsed = time.perf_counter() - start_time + + # Just ensure it completes in reasonable time and produces valid output + self.assertIsInstance(snapshot, set) + print( + f"\n[PERF] Materialise {len(times_to_check)} snapshots with {n_ids} ids: {elapsed:.4f}s" + ) + + def test_add_interval_performance_long_spans(self): + """Measure time to add long intervals (event-diff should be O(1)).""" + interval = IntervalPresenceStore() + n_intervals = 1000 + span_length = 10000 # very long interval + + start_time = time.perf_counter() + for i in range(n_intervals): + interval._add_interval(i, 0, span_length) + elapsed = time.perf_counter() - start_time + + # With event-diff, this should be fast (O(1) per interval) + print( + f"\n[PERF] Add {n_intervals} intervals of length {span_length}: {elapsed:.4f}s" + ) + self.assertLess(elapsed, 1.0, "Adding intervals should be fast with event-diff") + + def test_keys_performance_after_many_intervals(self): + """Measure time to call keys() after many interval operations.""" + interval = IntervalPresenceStore() + n_ids = 500 + intervals_per_id = 10 + + # Setup + for hid in range(n_ids): + for i in range(intervals_per_id): + start = hid * 50 + i * 10 + end = start + 5 + interval._add_interval(hid, start, end) + + # Benchmark keys() (triggers lazy rebuild) + start_time = time.perf_counter() + keys_list = list(interval.keys()) + elapsed = time.perf_counter() - start_time + + print( + f"\n[PERF] keys() after {n_ids*intervals_per_id} intervals: {elapsed:.4f}s, {len(keys_list)} keys" + ) + self.assertIsInstance(keys_list, list) + + def test_comparative_dense_vs_interval(self): + """Compare dense vs interval for typical workload.""" + n_ids = 200 + span_length = 50 + + # Dense benchmark + dense = DensePresenceStore() + start_time = time.perf_counter() + for hid in range(n_ids): + for t in range(hid, hid + span_length): + dense.setdefault(t, set()).add(hid) + dense_add_time = time.perf_counter() - start_time + + start_time = time.perf_counter() + for t in [0, 100, 200, 300]: + _ = dense[t] + dense_query_time = time.perf_counter() - start_time + + # Interval benchmark + interval = IntervalPresenceStore() + start_time = time.perf_counter() + for hid in range(n_ids): + interval._add_interval(hid, hid, hid + span_length - 1) + interval_add_time = time.perf_counter() - start_time + + start_time = time.perf_counter() + for t in [0, 100, 200, 300]: + _ = interval[t] + interval_query_time = time.perf_counter() - start_time + + print( + f"\n[PERF] Dense: add={dense_add_time:.4f}s, query={dense_query_time:.4f}s" + ) + print( + f"[PERF] Interval: add={interval_add_time:.4f}s, query={interval_query_time:.4f}s" + ) + + # Interval add should be much faster for long spans + self.assertLess( + interval_add_time, + dense_add_time, + "Interval should be faster for adding long spans", + ) + + +if __name__ == "__main__": + unittest.main(verbosity=2) diff --git a/ash_model/test/unit/test_ash.py b/ash_model/test/unit/test_ash.py new file mode 100644 index 0000000..53ea88b --- /dev/null +++ b/ash_model/test/unit/test_ash.py @@ -0,0 +1,492 @@ +import json +import unittest + +from networkx.algorithms import bipartite +import networkx as nx + +from ash_model import ASH, NProfile + + +class ASHTestCase(unittest.TestCase): + def test_add_node(self): + a = ASH() + a.add_node(1, start=0, end=2, attr_dict={"label": "A"}) + self.assertEqual(a.has_node(1), True) + + a.add_node(2, start=4, end=10, attr_dict=NProfile(2, name="Giulio")) + self.assertEqual(a.has_node(2), True) + + def test_add_nodes(self): + a = ASH() + a.add_nodes( + [1, 2], + start=0, + end=2, + node_attr_dict={1: {"label": "A"}, 2: {"label": "B"}}, + ) + self.assertEqual(a.has_node(1), True) + self.assertEqual(a.has_node(2), True) + self.assertEqual(a.has_node(1, start=0), True) + self.assertEqual(a.has_node(1, start=3), False) + self.assertEqual(a.has_node(1, start=2), True) + self.assertEqual(a.avg_number_of_nodes(), 2) + + self.assertEqual(a.node_presence(1), [0, 1, 2]) + + self.assertEqual(a.coverage(), 1) + self.assertEqual(a.node_contribution(1), 1) + + def test_degree_dist(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([15, 25], 0) + a.add_hyperedge([1, 24, 34], 0) + a.add_hyperedge([1, 2, 5, 6], 0) + a.add_hyperedge([1, 2, 5], 1) + a.add_hyperedge([3, 4, 5, 10], 1) + a.add_hyperedge([3, 4, 5, 12], 1) + + self.assertDictEqual(a.degree_distribution(), {4: 2, 3: 2, 1: 7, 2: 1}) + self.assertDictEqual(a.degree_distribution(start=0), {3: 1, 2: 1, 1: 7}) + self.assertDictEqual( + a.degree_distribution(start=0, end=1), a.degree_distribution() + ) + + def test_node_attributes(self): + a = ASH() + a.add_node(1, start=0, end=2, attr_dict={"label": "A"}) + + attr = a.get_node_profile(1) + self.assertEqual(attr, NProfile(1, **{"label": "A"})) + + attr = a.get_node_profile(1, tid=0) + self.assertEqual(attr, NProfile(1, **{"label": "A"})) + + label = a.get_node_attribute(1, attr_name="label") + self.assertEqual(label, {0: "A", 1: "A", 2: "A"}) + + label = a.get_node_attribute(1, attr_name="label", tid=0) + self.assertEqual(label, "A") + + def test_node_profiles(self): + a = ASH() + a.add_node(1, start=0, end=2, attr_dict=NProfile(1, label="A")) + + attr = a.get_node_profile(1) + self.assertEqual(attr, NProfile(1, **{"label": "A"})) + attr = a.get_node_profile(1, tid=0) + self.assertEqual(attr, NProfile(1, **{"label": "A"})) + + label = a.get_node_attribute(1, attr_name="label") + self.assertEqual(label, {0: "A", 1: "A", 2: "A"}) + + label = a.get_node_attribute(1, attr_name="label", tid=0) + self.assertEqual(label, "A") + + a.add_node(1, start=3, end=4, attr_dict=NProfile(1, label="B")) + attr = a.get_node_profile(1, 3) + self.assertEqual(attr, NProfile(1, **{"label": "B"})) + + def test_nodes(self): + a = ASH() + a.add_node(1, start=0, end=0, attr_dict={"label": "A"}) + a.add_node(2, start=1, end=3, attr_dict={"label": "A"}) + a.add_node(3, start=3, end=4, attr_dict={"label": "A"}) + + self.assertEqual(a.nodes(), [1, 2, 3]) + self.assertEqual(a.nodes(start=0), [1]) + self.assertEqual(a.nodes(start=3), [2, 3]) + self.assertEqual(a.nodes(start=4), [3]) + + self.assertEqual(a.number_of_nodes(), 3) + self.assertEqual(a.number_of_nodes(start=0), 1) + self.assertEqual(a.number_of_nodes(start=0, end=2), 2) + + def test_hyperedge(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0, 1) + a.add_hyperedge([1, 2, 3], 6, 9) + a.add_hyperedge([1, 2, 3], -3, -2) + a.add_hyperedge([3, 4, 5], 3, 4) + + self.assertEqual(a.avg_number_of_hyperedges(), 1.0) + self.assertEqual(a.hyperedge_contribution("e1"), 0.8) + + self.assertEqual(a.has_hyperedge([1, 2, 3]), True) + self.assertEqual(a.has_hyperedge([1, 2, 4]), False) + self.assertEqual(a.has_hyperedge([1, 2, 3], start=0), True) + self.assertEqual(a.has_hyperedge([1, 2, 3], start=5), False) + + self.assertEqual(a.size(), 2) + self.assertEqual(a.size(0), 1) + + self.assertEqual(a.number_of_neighbors(1), 2) + self.assertEqual(a.number_of_neighbors(1, hyperedge_size=3), 2) + self.assertEqual(a.number_of_neighbors(1, hyperedge_size=4), 0) + self.assertEqual(a.number_of_neighbors(1, start=0), 2) + self.assertEqual(a.number_of_neighbors(1, start=100), 0) + + self.assertEqual(a.degree(1), 1) + self.assertEqual(a.degree(1, hyperedge_size=3), 1) + self.assertEqual(a.degree(1, hyperedge_size=4), 0) + self.assertEqual(a.degree(1, start=0), 1) + self.assertEqual(a.degree(1, start=100), 0) + + hs = a.hyperedges() + self.assertEqual(len(hs), 2) + self.assertEqual(sorted(hs), ["e1", "e2"]) + hs = a.hyperedges(start=4) + self.assertEqual(hs, ["e2"]) + + hs = a.hyperedges(hyperedge_size=3) + self.assertEqual(sorted(hs), ["e1", "e2"]) + hs = a.hyperedges(hyperedge_size=4) + self.assertEqual(hs, list()) + hs = a.hyperedges(hyperedge_size=3, start=4) + self.assertEqual(hs, ["e2"]) + hs = a.hyperedges(hyperedge_size=2, start=4) + self.assertEqual(hs, list()) + + a.add_hyperedges([[4, 5], [6, 7], [8, 9, 10]], start=3, end=10) + hs = a.hyperedges() + self.assertEqual(len(hs), 5) + self.assertEqual(sorted(hs), ["e1", "e2", "e3", "e4", "e5"]) + + self.assertEqual(a.get_hyperedge_id([1, 2, 3]), "e1") + self.assertEqual(a.get_hyperedge_nodes("e1"), frozenset([1, 2, 3])) + + # self.assertEqual(a.get_hyperedge_weight("e1"), 3) + a.add_hyperedge([1, 2, 3], 9, 11) + # self.assertEqual(a.get_hyperedge_weight("e1"), 4) + + self.assertEqual(a.has_hyperedge([1, 2, 3]), True) + self.assertEqual(a.has_hyperedge([1, 2, 3, 4]), False) + self.assertEqual(a.has_hyperedge([1, 2, 3], start=0), True) + self.assertEqual(a.has_hyperedge([1, 2, 3], start=100), False) + + self.assertEqual(a.has_hyperedge("e1"), True) + self.assertEqual(a.has_hyperedge("e9"), False) + self.assertEqual(a.has_hyperedge("e1", start=0), True) + self.assertEqual(a.has_hyperedge("e1", start=100), False) + + self.assertEqual(a.uniformity(), 0.4845360824742268) + + a = ASH() + a.add_hyperedge([1, 2, 3], 0, 1) + a.add_hyperedge([1, 4], 0, 2) + a.add_hyperedge([1, 2, 4], 2, 3) + + self.assertEqual(sorted(a.hyperedges()), ["e1", "e2", "e3"]) + self.assertEqual(sorted(list(a.hyperedges(start=0))), ["e1", "e2"]) + self.assertEqual(sorted(list(a.hyperedges(start=2))), ["e2", "e3"]) + self.assertEqual(sorted(list(a.hyperedges(start=3))), ["e3"]) + self.assertEqual(sorted(list(a.hyperedges(start=2, end=3))), ["e2", "e3"]) + + self.assertEqual(sorted(list(a.hyperedges(start=3, end=3))), ["e3"]) + + def test_temporal_slice(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0, 1) + a.add_hyperedge([1, 2, 3], 6, 9) + a.add_hyperedge([1, 2, 5], 5, 10) + a.add_hyperedge([3, 4, 5], 3, 4) + + b, old_to_new = a.temporal_slice(0) + self.assertIsInstance(b, ASH) + self.assertEqual(b.nodes(), [1, 2, 3]) + + b, old_to_new = a.temporal_slice(0, 0) + self.assertIsInstance(b, ASH) + self.assertEqual(b.nodes(), [1, 2, 3]) + + c, old_to_new = a.temporal_slice(5, 7) + self.assertIsInstance(c, ASH) + self.assertEqual(sorted(c.nodes()), [1, 2, 3, 5]) + + def test_interactions(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0, 1) + a.add_hyperedge([1, 2, 3], 6, 9) + a.add_hyperedge([1, 2, 5], 5, 10) + a.add_hyperedge([3, 4, 5], 3, 4) + + for he in a.stream_interactions(): + self.assertEqual(len(he), 3) + + def test_size_distribution(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([15, 25], 0) + a.add_hyperedge([1, 24, 34], 0) + a.add_hyperedge([1, 2, 5, 6], 0) + a.add_hyperedge([1, 2, 5], 1) + a.add_hyperedge([3, 4, 5, 10], 1) + a.add_hyperedge([3, 4, 5, 12], 1) + + self.assertDictEqual(a.hyperedge_size_distribution(), {2: 1, 3: 3, 4: 3}) + self.assertDictEqual(a.hyperedge_size_distribution(start=0), {2: 1, 3: 2, 4: 1}) + self.assertDictEqual( + a.hyperedge_size_distribution(start=0, end=1), {2: 1, 3: 3, 4: 3} + ) + + self.assertEqual(a.degree_by_hyperedge_size(1), {3: 3, 4: 1}) + self.assertEqual(a.degree_by_hyperedge_size(1, start=1), {3: 1}) + + self.assertEqual(a.s_degree(1, 4), 1) + self.assertEqual(a.s_degree(1, 4, 0), 1) + + def test_star(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([15, 25], 0) + a.add_hyperedge([1, 24, 34], 0) + a.add_hyperedge([1, 2, 5, 6], 0) + a.add_hyperedge([1, 2, 5], 1) + a.add_hyperedge([3, 4, 5, 10], 1) + a.add_hyperedge([3, 4, 5, 12], 1) + + self.assertEqual(sorted(a.star(1)), ["e1", "e3", "e4", "e5"]) + self.assertEqual(sorted(a.star(1, start=0)), ["e1", "e3", "e4"]) + self.assertEqual(a.star(1, start=0, hyperedge_size=4), ["e4"]) + + def test_line_graph(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([2, 3, 4], 0) + a.add_hyperedge([1, 3], 1) + a.add_hyperedge([3, 4], 1) + + g = a.s_line_graph() + g2 = nx.Graph() + edges = [ + ("e1", "e2"), + ("e1", "e4"), + ("e1", "e3"), + ("e1", "e5"), + ("e2", "e3"), + ("e2", "e4"), + ("e2", "e5"), + ("e3", "e4"), + ("e3", "e5"), + ("e4", "e5"), + ] + g2.add_edges_from(edges) + + self.assertEqual(nx.is_isomorphic(g, g2), True) + + g = a.s_line_graph(start=0, end=0) + + eds = sorted([("e1", "e2"), ("e1", "e3"), ("e2", "e3")]) + res = sorted([tuple(sorted(i)) for i in list(g.edges())]) + + self.assertListEqual(res, eds) + + def test_bipartite(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([2, 3, 4], 0) + a.add_hyperedge([1, 3], 1) + a.add_hyperedge([3, 4], 1) + + g = a.bipartite_projection() + self.assertEqual(bipartite.is_bipartite(g), True) + edges, nodes = bipartite.sets(g) + self.assertEqual(sorted(edges), ["e1", "e2", "e3", "e4", "e5"]) + self.assertEqual(sorted(nodes), [1, 2, 3, 4]) + + g = a.bipartite_projection(start=0, end=0) + self.assertEqual(bipartite.is_bipartite(g), True) + + def test_dual(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([2, 3, 4], 0) + a.add_hyperedge([1, 3], 1) + a.add_hyperedge([3, 4], 1) + + dual, mapping = a.dual_hypergraph() + self.assertIsInstance(dual, ASH) + self.assertEqual(dual.number_of_nodes(), 5) + self.assertEqual(dual.number_of_hyperedges(), 4) + + def test_s_incident(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([1, 2, 4], 0) + + self.assertEqual(sorted(a.get_s_incident("e1", s=1)), [("e2", 1), ("e3", 2)]) + self.assertEqual(sorted(a.get_s_incident("e1", s=2)), [("e3", 2)]) + self.assertEqual(sorted(a.get_s_incident("e1", s=3)), []) + + def test_hyper_subgraph(self): + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([2, 3, 4], 0) + a.add_hyperedge([1, 3], 1) + a.add_hyperedge([3, 4], 1) + + a.add_node(1, start=0, end=1, attr_dict=NProfile(node_id=1, party="L", age=37)) + a.add_node(1, start=0, end=1, attr_dict=NProfile(node_id=2, party="L", age=20)) + + b, eid_map = a.induced_hypergraph(("e1", "e2")) + self.assertEqual(len(eid_map), 2) + + def test_removal(self): + for backend in ["dense", "interval"]: + + a = ASH(backend=backend) + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([2, 3, 4], 0) + a.add_hyperedge([1, 3], 1) + a.add_hyperedge([3, 4], 1) + a.add_hyperedge([3, 4], 2) + + a.remove_hyperedge("e1") + self.assertEqual(a.has_hyperedge("e1"), False) + self.assertEqual(len(a.hyperedges()), 4) + + a.remove_hyperedge("e5", start=0) + self.assertEqual(a.has_hyperedge("e5"), True) + self.assertEqual(a.has_hyperedge("e5", start=0), False) + self.assertEqual(a.has_hyperedge("e5", start=1), True) + + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([2, 3, 4], 0) + a.add_hyperedge([1, 3], 1) + a.add_hyperedge([3, 4], 1) + a.add_hyperedge([3, 4], 2) + + a.remove_node(1) + self.assertEqual(a.has_node(1), False) + self.assertEqual(len(a.nodes()), 3) + self.assertEqual(len(a.hyperedges()), 2) + + a.add_node( + 1, start=0, end=1, attr_dict=NProfile(node_id=1, party="L", age=37) + ) + a.remove_unlabelled_nodes("party") + self.assertEqual(len(a.nodes()), 1) + + +class ASHAdditionalTests(unittest.TestCase): + + def test_edge_attributes_and_weights(self): + a = ASH() + # add with two attributes + a.add_hyperedge([1, 2], start=0, weight=5, label="x") + # full‐history attribute dict + self.assertEqual(a.get_hyperedge_attribute("e1", "weight"), 5) + # single‐snapshot access + self.assertEqual(a.get_hyperedge_attribute("e1", "weight"), 5) + # get all attrs + self.assertEqual(a.get_hyperedge_attributes("e1"), {"weight": 5, "label": "x"}) + # get all attrs + attrs = a.get_hyperedge_attributes("e1") + self.assertIn("label", attrs) + + # list names of attributes + all_attrs = a.list_hyperedge_attributes() + self.assertIn("weight", all_attrs) + # categorical only (only string‐valued) + cat_attrs = a.list_hyperedge_attributes(categorical=True) + self.assertEqual(cat_attrs, {"label": {"x"}}) + # weight helper defaults to 1 if no weight set + b = ASH() + b.add_hyperedge([3, 4], 1) + self.assertEqual(b.get_hyperedge_weight("e1"), 1) + + def test_list_node_attributes_categorical(self): + a = ASH() + # two nodes with string labels and one with numeric + a.add_node(1, 0, attr_dict={"type": "A"}) + a.add_node(2, 0, attr_dict={"type": "B"}) + a.add_node(3, 1, attr_dict={"value": 42}) + all_attrs = a.list_node_attributes() + self.assertEqual(all_attrs["type"], {"A", "B"}) + self.assertEqual(all_attrs["value"], {42}) + # categorical only should drop 'value' + cat = a.list_node_attributes(categorical=True) + self.assertEqual(cat, {"type": {"A", "B"}}) + # time‐slice + self.assertEqual(a.list_node_attributes(tid=1), {"value": {42}}) + + def test_presence_and_intervals(self): + a = ASH() + # two discontiguous spans for node 1 + a.add_node(1, 0) + a.add_node(1, 2) + self.assertEqual(a.node_presence(1), [0, 2]) + self.assertEqual(a.node_presence(1, as_intervals=True), [(0, 0), (2, 2)]) + # same for hyperedges + b = ASH() + b.add_hyperedge([1, 2, 3], 0) + b.add_hyperedge([1, 2, 3], 2) + self.assertEqual(b.hyperedge_presence("e1"), [0, 2]) + self.assertEqual( + b.hyperedge_presence("e1", as_intervals=True), [(0, 0), (2, 2)] + ) + + def test_empty_statistics(self): + a = ASH() + # no snapshots → all averages and ratios are zero + self.assertEqual(a.avg_number_of_nodes(), 0.0) + self.assertEqual(a.avg_number_of_hyperedges(), 0.0) + self.assertEqual(a.coverage(), 0.0) + self.assertEqual(a.uniformity(), 0.0) + + def test_remove_nodes_and_hyperedges_helpers(self): + a = ASH() + a.add_hyperedge([1, 2], 0) + a.add_node(3, 0) + # remove multiple nodes + a.remove_nodes([1, 3]) + self.assertFalse(a.has_node(1)) + self.assertFalse(a.has_node(3)) + # the only hyperedge depended on node 1 should be gone + self.assertFalse(a.has_hyperedge("e1")) + # remove multiple hyperedges + b = ASH() + b.add_hyperedge([1, 2], 0) + b.add_hyperedge([2, 3], 0) + b.remove_hyperedges(["e1", "e2"]) + self.assertEqual(b.hyperedges(), []) + + def test_serialization_to_dict_and_str(self): + a = ASH() + a.add_hyperedge([1, 2], 0) + a.add_node(1, 0, attr_dict={"name": "Alice"}) + d = a.to_dict() + # hedges and nodes keys exist + self.assertIn("hedges", d) + self.assertIn("nodes", d) + # presence intervals injected + hedge_data = d["hedges"]["e1"] + self.assertIn("_presence", hedge_data["attributes"]) + + # node attributes are present + node_data = d["nodes"][1] # node 1 at time 0 + self.assertEqual(node_data, {0: {"name": "Alice"}}) + # string repr mentions core stats + s = str(a) + self.assertIn("Attributed Stream Hypergraph", s) + self.assertIn("Nodes: 2", s) + self.assertIn("Hyperedges: 1", s) + + def test_to_dict_roundtrip_consistency(self): + # ensure to_dict returns a pure‐python serializable structure + a = ASH() + a.add_hyperedge([1, 2], 0) + a.add_node(1, 0, attr_dict=NProfile(1, foo=10)) + d1 = a.to_dict() + s = json.dumps(d1) # must be JSON-serializable + d2 = json.loads(s) + self.assertEqual(set(d2["hedges"].keys()), {"e1"}) + self.assertEqual(set(d2["nodes"].keys()), {"1", "2"}) diff --git a/ash_model/test/test_nprofile.py b/ash_model/test/unit/test_nprofile.py similarity index 97% rename from ash_model/test/test_nprofile.py rename to ash_model/test/unit/test_nprofile.py index a085b29..3c0b4c5 100644 --- a/ash_model/test/test_nprofile.py +++ b/ash_model/test/unit/test_nprofile.py @@ -1,9 +1,11 @@ import unittest -from ash_model import NProfile + +from ash_model import NProfile, ASH class NProfileTestCase(unittest.TestCase): def test_profile(self): + p = NProfile(node_id=1) p.add_attribute("name", "Giulio") p.add_attribute("age", 37) @@ -22,6 +24,7 @@ def test_profile(self): self.assertEqual(p.has_attribute("location"), True) def test_compare(self): + p = NProfile(node_id=1) p.add_attributes(age=20, opinion=1) diff --git a/ash_model/test/utils/__init__.py b/ash_model/test/utils/__init__.py new file mode 100644 index 0000000..505c200 --- /dev/null +++ b/ash_model/test/utils/__init__.py @@ -0,0 +1 @@ +"""Tests for utility functions (matrices, projections, conversions).""" diff --git a/ash_model/test/utils/test_utils.py b/ash_model/test/utils/test_utils.py new file mode 100644 index 0000000..b51aea5 --- /dev/null +++ b/ash_model/test/utils/test_utils.py @@ -0,0 +1,568 @@ +import unittest +from typing import Any + +import networkx as nx +import numpy as np +from scipy import sparse + +import ash_model.utils as ut +from ash_model import ASH, NProfile +from ash_model.utils import ( + aggregate_node_profile, + bipartite_projection, + bipartite_projection_by_time, + clique_projection, + clique_projection_by_time, + dual_hypergraph_projection, + dual_hypergraph_projection_by_time, + hyperedge_aggregate_node_profile, + line_graph_projection, + line_graph_projection_by_time, +) + + +def get_hypergraph() -> ASH: + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([15, 25], 0) + a.add_hyperedge([1, 24, 34], 0) + a.add_hyperedge([1, 2, 5, 6], 0) + a.add_hyperedge([1, 2, 5], 1) + a.add_hyperedge([3, 4, 5, 10], 1) + a.add_hyperedge([3, 4, 5, 12], 1) + return a + + +class MatricesTestCase(unittest.TestCase): + + def setUp(self): + self.h = get_hypergraph() + + def test_incidence(self): + # global incidence covers all snapshots (0 and 1) + M = ut.incidence_matrix(self.h) + + # There are 9 unique nodes at t=0 plus possibly new at t=1 (node 4,10,12) + # Unique nodes overall: {1,2,3,5,6,15,24,25,34,4,10,12} => 12 + # Total hyperedges overall: 7 + self.assertIsInstance(M, sparse.csr_matrix) + self.assertEqual(M.shape, (12, 7)) + + # check that all nodes and hyperedges are present + node_map = ut.get_node_id_mapping(self.h) + he_map = ut.get_hyperedge_id_mapping(self.h) + + for edge in self.h.hyperedges(): + eidx = he_map[edge] + for node in self.h.get_hyperedge_nodes(edge): + nidx = node_map[node] + # check that the incidence matrix has a 1 at (node, edge) + self.assertEqual(M[nidx, eidx], 1) + + # check that the incidence matrix has 0s where it should + for node in self.h.nodes(): + if node not in self.h.get_hyperedge_nodes(edge): + nidx = node_map[node] + self.assertEqual(M[nidx, eidx], 0) + + def test_incidence_by_time(self): + mats = ut.incidence_matrix_by_time(self.h) + # should have two keys: 0 and 1 + self.assertCountEqual(list(mats.keys()), [0, 1]) + node_map = ut.get_node_id_mapping(self.h) + he_map = ut.get_hyperedge_id_mapping(self.h) + for t in [0, 1]: + M = mats[t] + self.assertIsInstance(M, sparse.csr_matrix) + + # shape + self.assertEqual(M.shape, (12, 7)) + + # check that if a node is in a hyperedge at time t, it has a 1 in the incidence matrix, else 0 + for edge in self.h.hyperedges(start=t, end=t): + eidx = he_map[edge] + for node in self.h.get_hyperedge_nodes(edge): + nidx = node_map[node] + self.assertEqual(M[nidx, eidx], 1) + + # check that the incidence matrix has 0s where it should + for node in self.h.nodes(): + if node not in self.h.get_hyperedge_nodes(edge): + nidx = node_map[node] + self.assertEqual(M[nidx, eidx], 0) + + def test_adjacency_global(self): + A = ut.adjacency_matrix(self.h) + self.assertIsInstance(A, sparse.csr_matrix) + # adjacency is symmetric, shape 12×12, diagonal zeros + self.assertEqual(A.shape, (12, 12)) + self.assertTrue((A.diagonal() == 0).all()) + + node_map = ut.get_node_id_mapping(self.h) + i1, i2 = node_map[1], node_map[2] + i15, i25 = node_map[15], node_map[25] + # Nodes 1 and 2 share three edges total ([1,2,3], [1,2,5,6], [1,2,5]) + self.assertEqual(A[i1, i2], 3) + # 15 and 25 only share the one edge at t=0 + self.assertEqual(A[i15, i25], 1) + # 1 and 15 never co-occur + self.assertEqual(A[i1, i15], 0) + + def test_adjacency_by_time(self): + ams = ut.adjacency_matrix_by_time(self.h) + self.assertCountEqual(list(ams.keys()), [0, 1]) + + for t in [0, 1]: + A = ams[t] + self.assertIsInstance(A, sparse.csr_matrix) + + # for each time step, the diagonal should be zero + self.assertTrue((A.diagonal() == 0).all()) + + # check that all node pairs that share an edge have a non-zero value + node_map = ut.get_node_id_mapping(self.h) + + # check that nodes that are not connected have a zero value + for node in self.h.nodes(): + nidx = node_map[node] + for other_node in self.h.nodes(): + if node != other_node: + other_nidx = node_map[other_node] + if A[nidx, other_nidx] > 0: + # they should be connected by at least one edge + connected = False + for edge in self.h.hyperedges(start=t, end=t, as_ids=False): + if node in edge and other_node in edge: + connected = True + break + self.assertTrue(connected) + else: + # they should not be connected by any edge + connected = False + for edge in self.h.hyperedges(start=t, end=t, as_ids=False): + if node in edge and other_node in edge: + connected = True + break + self.assertFalse(connected) + + +class MatricesReturnMappingTestCase(unittest.TestCase): + def setUp(self): + self.h = get_hypergraph() + + def test_incidence_with_mapping(self): + M, node_map, he_map = ut.incidence_matrix(self.h, return_mapping=True) + self.assertIsInstance(M, sparse.csr_matrix) + self.assertIsInstance(node_map, dict) + self.assertIsInstance(he_map, dict) + # shapes consistent with maps + self.assertEqual(M.shape, (len(node_map), len(he_map))) + # maps cover all nodes/hyperedges + self.assertCountEqual(node_map.keys(), self.h.nodes()) + self.assertCountEqual(he_map.keys(), self.h.hyperedges()) + + def test_incidence_by_time_with_mapping(self): + mats, node_map, he_map = ut.incidence_matrix_by_time( + self.h, return_mapping=True + ) + self.assertSetEqual(set(mats.keys()), set(self.h.temporal_snapshots_ids())) + for t, M in mats.items(): + self.assertIsInstance(M, sparse.csr_matrix) + self.assertEqual(M.shape, (len(node_map), len(he_map))) + + def test_adjacency_with_mapping(self): + A, node_map, he_map = ut.adjacency_matrix(self.h, return_mapping=True) + self.assertIsInstance(A, sparse.csr_matrix) + self.assertEqual(A.shape, (len(node_map), len(node_map))) + # he_map is returned for symmetry with incidence; must map all hyperedges + self.assertCountEqual(he_map.keys(), self.h.hyperedges()) + + def test_adjacency_by_time_with_mapping(self): + ams, node_map = ut.adjacency_matrix_by_time(self.h, return_mapping=True) + self.assertSetEqual(set(ams.keys()), set(self.h.temporal_snapshots_ids())) + for t, A in ams.items(): + self.assertIsInstance(A, sparse.csr_matrix) + self.assertEqual(A.shape, (len(node_map), len(node_map))) + + +class TestCliqueProjection(unittest.TestCase): + def setUp(self): + # build hypergraph with overlapping hyperedges at time 0 + self.h = ASH() + # nodes 1–3 in a triangle and 2–4 in an edge + self.h.add_hyperedge([1, 2, 3], start=0) + self.h.add_hyperedge([2, 4], start=0) + # attach a node attribute for testing keep_attrs + for n in [1, 2, 3, 4]: + self.h.add_node(n, start=0, attr_dict=NProfile(n, color=str(n))) + + def test_structure_default(self): + G = clique_projection(self.h, start=0, end=0, keep_attrs=False) + + expected = [ + (1, 2), + (1, 3), + (2, 3), + (2, 4), + ] + edges = sorted([tuple(sorted((u, v))) for u, v in G.edges()]) + self.assertListEqual(edges, expected) + + def test_keep_attrs(self): + G = clique_projection(self.h, start=0, end=0, keep_attrs=True) + # node attributes should propagate + for n in G.nodes(): + self.assertEqual(G.nodes[n][0]["color"], str(n)) + + def test_by_time(self): + # add hyperedge at time 1 + self.h.add_hyperedge([1, 4], start=1) + by_time = clique_projection_by_time(self.h, keep_attrs=False) + # should have entries for times 0 and 1 + self.assertCountEqual(list(by_time.keys()), [0, 1]) + # compare each to direct call + for t, Gt in by_time.items(): + direct = clique_projection(self.h, start=t, end=t) + self.assertTrue( + nx.is_isomorphic( + Gt, direct, edge_match=lambda a, b: a["weight"] == b["weight"] + ) + ) + + +class TestBipartiteProjection(unittest.TestCase): + def setUp(self): + self.h = ASH() + # two hyperedges at t=0 + self.h.add_hyperedge([1, 2], start=0) + self.h.add_hyperedge([2, 3], start=0) + # node attributes + for n in [1, 2, 3]: + self.h.add_node(n, start=0, attr_dict=NProfile(n, label=f"N{n}")) + + def test_structure_default(self): + G = bipartite_projection(self.h, start=0, end=0, keep_attrs=False) + # check bipartite sets + nodes = {n for n, d in G.nodes(data=True) if d.get("bipartite") == 0} + edges = {n for n, d in G.nodes(data=True) if d.get("bipartite") == 1} + self.assertEqual(nodes, {1, 2, 3}) + # hyperedge IDs are strings like 'e1','e2' + self.assertEqual(edges, {"e1", "e2"}) + # edges connect each node to its hyperedges + for he in edges: + members = set(self.h.get_hyperedge_nodes(he)) + self.assertEqual(set(G.neighbors(he)), members) + + def test_keep_attrs(self): + G = bipartite_projection(self.h, start=0, end=0, keep_attrs=True) + # only graph-nodes corresponding to ASH nodes get attrs + + for n in [1, 2, 3]: + attrs = self.h.get_node_attributes(n) + attrs["bipartite"] = 0 # add bipartite attr + self.assertEqual(G.nodes[n], attrs) + + def test_by_time(self): + self.h.add_hyperedge([3, 4], start=1) + by_time = bipartite_projection_by_time(self.h, keep_attrs=False) + self.assertCountEqual(list(by_time.keys()), [0, 1]) + for t, Gt in by_time.items(): + direct = bipartite_projection(self.h, start=t, end=t) + self.assertTrue(nx.is_isomorphic(Gt, direct)) + + +class TestLineGraphProjection(unittest.TestCase): + def setUp(self): + self.h = ASH() + # three hyperedges at t=0 + self.h.add_hyperedge([1, 2], start=0) # e1 + self.h.add_hyperedge([2, 3], start=0) # e2 + self.h.add_hyperedge([4, 5], start=0) # e3 + + def test_default_s1(self): + G = line_graph_projection(self.h, s=1, start=0, end=0, keep_attrs=False) + self.assertListEqual(sorted(G.nodes()), ["e1", "e2", "e3"]) + # e1 and e2 share node 2 + self.assertIn(("e1", "e2"), G.edges()) + # no edge between e1 and e3 + self.assertNotIn(("e1", "e3"), G.edges()) + + def test_s2_threshold(self): + # add a hyperedge sharing two nodes with e1 + self.h.add_hyperedge([1, 2, 6], start=0) # e4 + G = line_graph_projection(self.h, s=2, start=0, end=0) + # only e1 and e4 share two nodes + self.assertIn(("e1", "e4"), G.edges()) + self.assertNotIn(("e2", "e4"), G.edges()) + + def test_by_time(self): + self.h.add_hyperedge([2, 3], start=1) + by_time = line_graph_projection_by_time(self.h, s=1, keep_attrs=False) + self.assertCountEqual(list(by_time.keys()), [0, 1]) + for t, Gt in by_time.items(): + direct = line_graph_projection(self.h, s=1, start=t, end=t) + self.assertTrue(nx.is_isomorphic(Gt, direct)) + + +class TestDualHypergraphProjection(unittest.TestCase): + def setUp(self): + self.h = ASH() + # hyperedges at t=0 + self.h.add_hyperedge([1, 2], start=0) # original edge e1 + self.h.add_hyperedge([2, 3], start=0) # e2 + + def test_dual_structure(self): + dual, mapping = dual_hypergraph_projection(self.h, start=0, end=0) + # mapping maps original nodes to dual hyperedge IDs + self.assertEqual(set(mapping.keys()), {1, 2, 3}) + # dual hyperedges correspond to original nodes + for node, new_eid in mapping.items(): + members = set(dual.get_hyperedge_nodes(new_eid)) + # should be the list of original hyperedges containing 'node' + expected = { + he + for he in self.h.hyperedges(0, 0) + if node in self.h.get_hyperedge_nodes(he) + } + self.assertEqual(members, expected) + + def test_by_time(self): + # add an edge at time 1 + self.h.add_hyperedge([3, 4], start=1) + by_time = dual_hypergraph_projection_by_time(self.h) + self.assertCountEqual(list(by_time.keys()), [0, 1]) + for t, (dual_t, mapping_t) in by_time.items(): + dual_direct, map_direct = dual_hypergraph_projection(self.h, start=t, end=t) + self.assertCountEqual(mapping_t.items(), map_direct.items()) + # compare dual hyperedge memberships + for new_eid in mapping_t.values(): + self.assertEqual( + set(dual_t.get_hyperedge_nodes(new_eid)), + set(dual_direct.get_hyperedge_nodes(new_eid)), + ) + + +class TestFromNetworkxGraph(unittest.TestCase): + def test_type_error_on_non_graph(self): + with self.assertRaises(TypeError): + ut.from_networkx_graph("not a graph", start=0) + + def test_basic_conversion_without_attrs(self): + G = nx.Graph() + G.add_edges_from([(1, 2), (2, 3)]) + h = ut.from_networkx_graph(G, start=5, end=6, keep_attrs=False) + # hyperedges at t=5 and t=6 + hes5 = set(h.hyperedges(5, 6)) + self.assertEqual(len(hes5), 2) + expected = {frozenset({1, 2}), frozenset({2, 3})} + self.assertEqual({h.get_hyperedge_nodes(e) for e in hes5}, expected) + # nodes present both times, no attrs + for t in (5, 6): + self.assertCountEqual(h.nodes(t), [1, 2, 3]) + for n in h.nodes(t): + self.assertEqual(h.get_node_attributes(n, tid=t), {}) + + def test_basic_conversion_with_attrs(self): + G = nx.Graph() + G.add_node(1, color="red") + G.add_node(2, size=10) + G.add_edge(1, 2) + h = ut.from_networkx_graph(G, start=0, keep_attrs=True) + # node profiles at t=0 keep attrs + for n, data in G.nodes(data=True): + self.assertEqual(h.get_node_attributes(n, tid=0), data) + # one hyperedge + hes = h.hyperedges(0) + self.assertEqual(len(hes), 1) + he_nodes = h.get_hyperedge_nodes(hes[0]) + self.assertEqual(he_nodes, frozenset({1, 2})) + + +class TestFromNetworkxGraphList(unittest.TestCase): + def test_graph_list_conversion(self): + G0 = nx.Graph() + G0.add_edges_from([(1, 2)]) + G1 = nx.Graph() + G1.add_edges_from([(2, 3)]) + h = ut.from_networkx_graph_list([G0, G1], keep_attrs=False) + # time 0: one edge, nodes {1,2} + self.assertCountEqual(h.hyperedges(0), h.hyperedges(0, 0)) + self.assertCountEqual(h.nodes(0), [1, 2]) + # time 1: one edge, nodes {2,3} + self.assertCountEqual(h.hyperedges(1), h.hyperedges(1, 1)) + self.assertCountEqual(h.nodes(1), [2, 3]) + # global counts + self.assertEqual(len(h.hyperedges()), 2) + self.assertCountEqual(h.nodes(), [1, 2, 3]) + + +class TestFromNetworkxMaximalCliques(unittest.TestCase): + def test_type_error_on_non_graph(self): + with self.assertRaises(TypeError): + ut.from_networkx_maximal_cliques(123, start=0) + + def test_cliques_conversion(self): + G = nx.Graph() + # clique of size 3 and edge of size 2 + G.add_edges_from([(1, 2), (2, 3), (1, 3), (3, 4)]) + # add attr on node 4 + G.nodes[4]["role"] = "X" + h = ut.from_networkx_maximal_cliques(G, start=2, end=3) + # expected maximal cliques: {1,2,3} and {3,4} + expected = [set(c) for c in nx.find_cliques(G) if len(c) > 1] + hes = [set(h.get_hyperedge_nodes(e)) for e in h.hyperedges(2, 3)] + self.assertCountEqual(hes, expected) + # node attrs at t=2 and t=3 + for t in (2, 3): + for n, data in G.nodes(data=True): + self.assertEqual(h.get_node_attributes(n, tid=t), data) + + +class TestFromNetworkxMaximalCliquesList(unittest.TestCase): + def test_sequence_conversion(self): + G0 = nx.Graph() + G0.add_edges_from([(1, 2), (2, 3), (1, 3)]) + G1 = nx.Graph() + G1.add_edges_from([(3, 4)]) + h = ut.from_networkx_maximal_cliques_list([G0, G1]) + # time 0: one clique {1,2,3} + hes0 = [set(h.get_hyperedge_nodes(e)) for e in h.hyperedges(0, 0)] + self.assertEqual(hes0, [set([1, 2, 3])]) + # time 1: one clique {3,4} + hes1 = [set(h.get_hyperedge_nodes(e)) for e in h.hyperedges(1, 1)] + self.assertEqual(hes1, [set([3, 4])]) + # all nodes present across snapshots + self.assertCountEqual(h.nodes(), [1, 2, 3, 4]) + + +class TestFromNetworkxBipartite(unittest.TestCase): + def setUp(self): + # bipartite: nodes 1,2 on left; 'A','B' on right + self.G = nx.Graph() + left, right = {1, 2}, {"A", "B"} + self.G.add_nodes_from(left, bipartite=0) + self.G.add_nodes_from(right, bipartite=1) + self.G.add_edges_from([(1, "A"), (2, "A"), (2, "B")]) + + def test_type_error_on_non_graph(self): + with self.assertRaises(TypeError): + ut.from_networkx_bipartite("nope", start=0) + + def test_value_error_on_non_bipartite(self): + H = nx.Graph() + H.add_edges_from([(1, 2), (2, 3), (1, 3)]) + with self.assertRaises(ValueError): + ut.from_networkx_bipartite(H, start=0) + + def test_basic_bipartite_conversion(self): + h = ut.from_networkx_bipartite(self.G, start=7, end=8, keep_attrs=False) + # get bipartite sets + nodes, edges = nx.bipartite.sets(self.G) + # check nodes and hyperedges + self.assertListEqual(sorted(h.nodes()), sorted(list(nodes))) + self.assertListEqual(sorted(h.hyperedges()), ["e1", "e2"]) + + +class TestFromNetworkxBipartiteList(unittest.TestCase): + def test_sequence_bipartite_conversion(self): + h = get_hypergraph() + # make it connected + h.add_hyperedge(h.nodes(), start=0, end=1) + g = ut.bipartite_projection(h, keep_attrs=False) + + glist = [g, g.copy(), g.copy()] + + h2 = ut.from_networkx_bipartite_list(glist, keep_attrs=False) + self.assertListEqual(sorted(h2.nodes()), sorted(h.nodes())) + self.assertCountEqual(sorted(h2.hyperedges()), sorted(h.hyperedges())) + + # check time + self.assertListEqual(h2.temporal_snapshots_ids(), [0, 1, 2]) + for t in h.temporal_snapshots_ids(): + # all nodes present at each time step + self.assertCountEqual(h2.nodes(t), h2.nodes(t)) + # hyperedges are the same as in the bipartite projection + for he in h2.hyperedges(t): + nodes = h2.get_hyperedge_nodes(he) + # self.assertIn(set(nodes), [set(g.neighbors(r)) for r in g.nodes() if g.nodes[r]['bipartite'] == 1]) + + +class ProfileAggrTestCase(unittest.TestCase): + @staticmethod + def get_hypergraph() -> ASH: + a = ASH() + a.add_hyperedge([1, 2, 3], 0) + a.add_hyperedge([1, 4], 0) + a.add_hyperedge([1, 2, 3, 4], 0) + a.add_hyperedge([1, 3, 4], 1) + a.add_hyperedge([3, 4], 1) + + a.add_node( + 1, + start=0, + end=0, + attr_dict=NProfile(node_id=1, party="L", age=37, gender="M"), + ) + a.add_node( + 1, + start=1, + end=1, + attr_dict=NProfile(node_id=1, party="R", age=37, gender="M"), + ) + a.add_node( + 2, + start=0, + end=0, + attr_dict=NProfile(node_id=2, party="L", age=20, gender="F"), + ) + a.add_node( + 3, + start=0, + end=1, + attr_dict=NProfile(node_id=3, party="L", age=11, gender="F"), + ) + a.add_node( + 4, + start=0, + end=1, + attr_dict=NProfile(node_id=4, party="R", age=45, gender="M"), + ) + return a + + def test_aggregate_node_profile(self): + a = self.get_hypergraph() + # force deterministic categorical aggregation + prof = aggregate_node_profile( + a, 1, categorical_aggr="first", numerical_aggr="mean" + ) + attrs = dict(prof.items()) + self.assertEqual(attrs["party"], "L") # first of ['L','R'] + self.assertEqual(attrs["gender"], "M") # always 'M' + self.assertEqual(attrs["age"], 37.0) # mean of [37,37] + + def test_hyperedge_aggregate_node_profile(self): + a = self.get_hypergraph() + # pick the hyperedge [1,2,3] at time 0 + hes = list(a.hyperedges(start=0)) + he = next(h for h in hes if set(a.get_hyperedge_nodes(h)) == {1, 2, 3}) + + # aggregate all attributes at tid=0 + prof = hyperedge_aggregate_node_profile(a, he, 0) + items = dict(prof.items()) + # party mode is 'L', age mean=(37+20+11)/3 + self.assertEqual(items["party"], "L") + self.assertAlmostEqual(items["age"], (37 + 20 + 11) / 3) + + # check std was recorded + std = prof.get_statistic("age", "std")["std"] + self.assertAlmostEqual(std, np.std([37, 20, 11])) + + # test attr_name selection + prof2 = hyperedge_aggregate_node_profile(a, he, 0, attr_name="age") + items2 = dict(prof2.items()) + self.assertIn("age", items2) + self.assertEqual(len(items2), 1) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/viz/__init__.py b/ash_model/test/viz/__init__.py new file mode 100644 index 0000000..c348490 --- /dev/null +++ b/ash_model/test/viz/__init__.py @@ -0,0 +1 @@ +"""Tests for visualization functions.""" diff --git a/ash_model/test/viz/test_static_viz.py b/ash_model/test/viz/test_static_viz.py new file mode 100644 index 0000000..5108b94 --- /dev/null +++ b/ash_model/test/viz/test_static_viz.py @@ -0,0 +1,89 @@ +import unittest + +import matplotlib + +matplotlib.use("Agg") # headless + +from ash_model.classes import ASH +from ash_model.viz.static import ( + plot_s_degrees, + plot_hyperedge_size_distribution, + plot_degree_distribution, + plot_s_ranks, +) + + +class TestStaticViz(unittest.TestCase): + def setUp(self): + """Create a test hypergraph with varied structure.""" + self.h = ASH() + + # Create hyperedges with varying sizes + self.h.add_hyperedge([1, 2], 0, 5) + self.h.add_hyperedge([1, 3], 1, 4) + self.h.add_hyperedge([2, 3, 4], 2, 5) + self.h.add_hyperedge([4, 5], 5, 10) + self.h.add_hyperedge([5, 6, 7], 6, 9) + self.h.add_hyperedge([3, 4, 5], 5, 8) + self.h.add_hyperedge([7, 8], 10, 15) + self.h.add_hyperedge([6, 7, 8, 9], 11, 14) + self.h.add_hyperedge([1, 2, 3, 4, 5], 5, 10) + + def test_s_degrees_loglog(self): + """Test s-degrees plot with loglog scale.""" + ax = plot_s_degrees(self.h, smax=3, loglog=True) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_s_degrees_linear(self): + """Test s-degrees plot with linear scale.""" + ax = plot_s_degrees(self.h, smax=2, loglog=False) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_hyperedge_size_distribution(self): + """Test hyperedge size distribution plot.""" + ax = plot_hyperedge_size_distribution(self.h) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "patches")) + self.assertGreater(len(ax.patches), 0) + + def test_hyperedge_size_distribution_filtered(self): + """Test hyperedge size distribution with min/max filters.""" + ax = plot_hyperedge_size_distribution(self.h, min_size=2, max_size=4) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "patches")) + + def test_degree_distribution_loglog(self): + """Test degree distribution with loglog scale.""" + ax = plot_degree_distribution(self.h, loglog=True) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_degree_distribution_linear(self): + """Test degree distribution with linear scale.""" + ax = plot_degree_distribution(self.h, loglog=False) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_s_ranks_loglog(self): + """Test s-ranks plot with loglog scale.""" + ax = plot_s_ranks(self.h, smax=3, loglog=True) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_s_ranks_linear(self): + """Test s-ranks plot with linear scale.""" + ax = plot_s_ranks(self.h, smax=2, loglog=False) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/test/viz/test_temporal_viz.py b/ash_model/test/viz/test_temporal_viz.py new file mode 100644 index 0000000..df5ff8c --- /dev/null +++ b/ash_model/test/viz/test_temporal_viz.py @@ -0,0 +1,90 @@ +import unittest + +import matplotlib + +matplotlib.use("Agg") # headless + +from ash_model.classes import ASH +from ash_model.viz.temporal import ( + plot_hyperedge_activity_series, + plot_node_activity_series, + plot_presence_timeline, + plot_inter_event_time_distribution, + plot_hyperedge_lifespan_distribution, + plot_node_lifespan_distribution, +) + + +class TestTemporalViz(unittest.TestCase): + def setUp(self): + """Create a test hypergraph with temporal structure.""" + self.h = ASH() + # Build temporal structure with varied patterns + # Hyperedge e1: nodes 1,2 active t=0..2 + self.h.add_hyperedge([1, 2], 0, 2) + # Hyperedge e2: nodes 2,3 active t=1..3 + self.h.add_hyperedge([2, 3], 1, 3) + # Hyperedge e3: nodes 3,4 active t=3 only + self.h.add_hyperedge([3, 4], 3, 3) + # Hyperedge e4: nodes 1,3 active t=2..5 + self.h.add_hyperedge([1, 3], 2, 5) + # Hyperedge e5: larger hyperedge + self.h.add_hyperedge([1, 2, 3, 4], 4, 6) + + def test_hyperedge_activity_series(self): + """Test hyperedge activity series plot.""" + ax = plot_hyperedge_activity_series(self.h) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_hyperedge_activity_series_normalized(self): + """Test normalized hyperedge activity series plot.""" + ax = plot_hyperedge_activity_series(self.h, normalize=True) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_node_activity_series(self): + """Test node activity series plot.""" + ax = plot_node_activity_series(self.h) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_node_activity_series_normalized(self): + """Test normalized node activity series plot.""" + ax = plot_node_activity_series(self.h, normalize=True) + self.assertIsNotNone(ax) + self.assertTrue(hasattr(ax, "lines")) + self.assertGreater(len(ax.lines), 0) + + def test_presence_timeline_hyperedges(self): + """Test presence timeline for hyperedges.""" + hs = list(self.h.hyperedges()) + ax = plot_presence_timeline(self.h, hyperedges=hs) + self.assertIsNotNone(ax) + + def test_presence_timeline_nodes(self): + """Test presence timeline for nodes.""" + ax = plot_presence_timeline(self.h, nodes=[1, 2, 3]) + self.assertIsNotNone(ax) + + def test_inter_event_distribution(self): + """Test inter-event time distribution plot.""" + ax = plot_inter_event_time_distribution(self.h) + self.assertIsNotNone(ax) + + def test_hyperedge_lifespan_distribution(self): + """Test hyperedge lifespan distribution plot.""" + ax = plot_hyperedge_lifespan_distribution(self.h) + self.assertIsNotNone(ax) + + def test_node_lifespan_distribution(self): + """Test node lifespan distribution plot.""" + ax = plot_node_lifespan_distribution(self.h) + self.assertIsNotNone(ax) + + +if __name__ == "__main__": + unittest.main() diff --git a/ash_model/utils/__init__.py b/ash_model/utils/__init__.py index 4dc5abe..3b07338 100644 --- a/ash_model/utils/__init__.py +++ b/ash_model/utils/__init__.py @@ -1,2 +1,4 @@ -from .undirected_matrices import * -from .undirected_graph_transformations import * +from .matrices import * +from .projections import * +from .networkx import * +from .profiles import * diff --git a/ash_model/utils/matrices.py b/ash_model/utils/matrices.py new file mode 100644 index 0000000..a31b98d --- /dev/null +++ b/ash_model/utils/matrices.py @@ -0,0 +1,167 @@ +from typing import Dict, Optional, Tuple, Union +from scipy import sparse + +from ash_model import ASH + + +def get_hyperedge_id_mapping(h: ASH) -> Dict[int, int]: + """ + Returns a mapping of hyperedge IDs to indices and vice versa. + This function creates a mapping from hyperedge IDs to their respective indices + + :param h: The ASH object to be converted. + + :return: A dictionary mapping hyperedge IDs to indices. + """ + hyperedges = h.hyperedges(as_ids=True) + edge_to_index = {he: i for i, he in enumerate(sorted(hyperedges))} + return edge_to_index + + +def get_node_id_mapping(h: ASH) -> Dict[int, int]: + """ + Returns a mapping of node IDs to indices and vice versa. + + :param h: The ASH object to be converted. + + :return: A dictionary mapping node IDs to indices. + """ + nodes = h.nodes() + node_to_index = {node: i for i, node in enumerate(sorted(nodes))} + return node_to_index + + +def _build_incidence_matrix( + h: ASH, + node_to_index: Dict[int, int], + he_to_index: Dict[int, int], + start: int = None, + end: int = None, +) -> sparse.csr_matrix: + """ + Builds the incidence matrix for the ASH object using the provided mappings. + + :param h: The ASH object to be converted. + :param node_to_index: A mapping of node IDs to indices. + :param he_to_index: A mapping of hyperedge IDs to indices. + + :return: A sparse matrix representing the incidence matrix of the ASH. + """ + incidence = sparse.lil_matrix((len(node_to_index), len(he_to_index)), dtype=int) + + for he in h.hyperedges(start, end): + he_index = he_to_index[he] + for node in h.get_hyperedge_nodes(he): + node_index = node_to_index[node] + incidence[node_index, he_index] = 1 + + return incidence.tocsr() + + +def incidence_matrix( + h: ASH, + start: Optional[int] = None, + end: Optional[int] = None, + return_mapping: bool = False, +) -> Union[sparse.csr_matrix, Tuple[sparse.csr_matrix, Dict[int, int], Dict[str, int]]]: + """ + Returns the incidence matrix of the ASH object. + The incidence matrix is a sparse matrix where rows represent nodes and columns represent hyperedges. + The value is 1 if the node belongs to the hyperedge, 0 otherwise. + + :param h: The ASH object to be converted. + :param start: The start time of the projection (optional). + :param end: The end time of the projection (optional). + + :return: A sparse matrix representing the binary incidence matrix of the ASH. + """ + + # build index maps + node_to_index = get_node_id_mapping(h) + he_to_index = get_hyperedge_id_mapping(h) + + incidence = _build_incidence_matrix(h, node_to_index, he_to_index, start, end) + + if return_mapping: + return incidence, node_to_index, he_to_index + else: + return incidence + + +def incidence_matrix_by_time(h: ASH, return_mapping: bool = False) -> Union[ + Dict[int, sparse.csr_matrix], + Tuple[Dict[int, sparse.csr_matrix], Dict[int, int], Dict[str, int]], +]: + """ + Returns a dictionary of incidence matrices for each time step in the ASH object. + The keys are the time steps and the values are the corresponding incidence matrices. + + :param h: The ASH object to be converted. + + :return: A dictionary where keys are time steps and values are sparse matrices representing the incidence matrix. + """ + + incidence_matrices = {} + # + node_to_index = get_node_id_mapping(h) + he_to_index = get_hyperedge_id_mapping(h) + + for t in h.temporal_snapshots_ids(): + incidence = _build_incidence_matrix( + h, node_to_index, he_to_index, start=t, end=t + ) + incidence_matrices[t] = incidence.tocsr() + if return_mapping: + return incidence_matrices, node_to_index, he_to_index + else: + return incidence_matrices + + +def adjacency_matrix( + h: ASH, + start: Optional[int] = None, + end: Optional[int] = None, + return_mapping: bool = False, +) -> Union[sparse.csr_matrix, Tuple[sparse.csr_matrix, Dict[int, int]]]: + """ + Returns the adjacency matrix of the ASH object. + The adjacency matrix is a sparse matrix where rows and columns represent nodes, + and the value is 1 if there is a hyperedge connecting the two nodes, 0 otherwise. + + :param h: The ASH object to be converted. + :param start: The start time of the projection (optional). + :param end: The end time of the projection (optional). + + :return: A sparse matrix representing the adjacency matrix of the ASH. + """ + incidence = incidence_matrix(h, start, end, return_mapping=False) + adjacency = incidence @ incidence.transpose() + adjacency.setdiag(0) + if return_mapping: + return adjacency, get_node_id_mapping(h), get_hyperedge_id_mapping(h) + else: + return adjacency + + +def adjacency_matrix_by_time( + h: ASH, return_mapping: bool = False +) -> Union[ + Dict[int, sparse.csr_matrix], Tuple[Dict[int, sparse.csr_matrix], Dict[int, int]] +]: + """ + Returns a dictionary of adjacency matrices for each time step in the ASH object. + The keys are the time steps and the values are the corresponding adjacency matrices. + + :param h: The ASH object to be converted. + + :return: A dictionary where keys are time steps and values are sparse matrices representing the adjacency matrix. + """ + + adjacency_matrices = {} + for t in h.temporal_snapshots_ids(): + adjacency_matrices[t] = adjacency_matrix(h, t, t, return_mapping=False) + + if return_mapping: + return adjacency_matrices, get_node_id_mapping(h) + else: + return adjacency_matrices diff --git a/ash_model/utils/networkx.py b/ash_model/utils/networkx.py new file mode 100644 index 0000000..0afc06c --- /dev/null +++ b/ash_model/utils/networkx.py @@ -0,0 +1,237 @@ +import copy +from typing import Optional, Sequence, Union + +import networkx as nx +from ash_model import ASH, NProfile + + +def _validate_graph(graph: nx.Graph) -> None: + """ + Ensure the input is an undirected NetworkX Graph. + + :raises TypeError: if not a networkx.Graph instance. + """ + if not isinstance(graph, nx.Graph): + raise TypeError("Transformation only applicable to undirected NetworkX Graphs") + + +def _add_nodes( + ash: ASH, + graph: nx.Graph, + start: int, + end: Optional[int], + keep_attrs: bool, + bipartite: bool = False, +) -> None: + """ + Add nodes from a NetworkX Graph to an ASH instance. + + :param ash: Target ASH object. + :param graph: Source NetworkX Graph. + :param start: Start time for node presence. + :param end: Optional end time for node presence. + :param keep_attrs: If True, preserves original node attributes. + """ + + if not bipartite: + node_data = graph.nodes(data=True) + else: + # For bipartite graphs, we only want the nodes from one partition + nodes, _ = nx.algorithms.bipartite.sets(graph) + node_data = ((node, graph.nodes[node]) for node in nodes) + + for node, data in node_data: + if keep_attrs: + attrs = copy.copy(data) + profile = NProfile(node, **attrs) + ash.add_node(node, start=start, end=end, attr_dict=profile) + else: + ash.add_node(node, start=start, end=end) + + +def _add_hyperedges( + ash: ASH, + graph: nx.Graph, + start: int, + end: Optional[int], +) -> None: + """ + Add each edge of a NetworkX Graph as a 2-node hyperedge to an ASH instance. + + :param ash: Target ASH object. + :param graph: Source NetworkX Graph. + :param start: Start time for hyperedges. + :param end: Optional end time for hyperedges. + """ + for u, v in graph.edges(): + ash.add_hyperedge([u, v], start=start, end=end) + + +def from_networkx_graph( + graph: nx.Graph, + start: int, + end: Optional[int] = None, + keep_attrs: bool = False, +) -> ASH: + """ + Convert an undirected NetworkX Graph into an ASH with 2-node hyperedges. + + :param graph: Undirected NetworkX Graph. + :param start: Start time of hyperedges and nodes. + :param end: Optional end time of hyperedges and nodes. + :param keep_attrs: If True, node attributes are preserved. + + :return: Populated ASH object. + """ + _validate_graph(graph) + ash = ASH() + _add_nodes(ash, graph, start, end, keep_attrs) + _add_hyperedges(ash, graph, start, end) + return ash + + +def from_networkx_graph_list( + graphs: Sequence[nx.Graph], + keep_attrs: bool = False, +) -> ASH: + """ + Convert a sequence of NetworkX Graphs into a time­-sliced ASH. + + Each graph corresponds to a snapshot: its index is the start time. + + :param graphs: Sequence of undirected NetworkX Graphs. + :param keep_attrs: If True, node attributes are preserved. + + :return: Populated ASH with hyperedges from each snapshot. + """ + ash = ASH() + for t, graph in enumerate(graphs): + _validate_graph(graph) + _add_nodes(ash, graph, t, t, keep_attrs) + _add_hyperedges(ash, graph, t, t) + return ash + + +def from_networkx_maximal_cliques( + graph: nx.Graph, + start: int, + end: Optional[int] = None, +) -> ASH: + """ + Convert maximal cliques of a NetworkX Graph into an ASH. + + :param graph: Undirected NetworkX Graph. + :param start: Start time of clique hyperedges. + :param end: Optional end time of clique hyperedges. + + :return: ASH object with each maximal clique as a hyperedge. + """ + _validate_graph(graph) + ash = ASH() + # add only cliques of size >1 + for clique in nx.find_cliques(graph): + if len(clique) > 1: + ash.add_hyperedge(clique, start=start, end=end) + # add all nodes with profiles + for node, data in graph.nodes(data=True): + ash.add_node( + node, start=start, end=end, attr_dict=NProfile(node, **copy.copy(data)) + ) + return ash + + +def from_networkx_maximal_cliques_list(graphs: Sequence[nx.Graph]) -> ASH: + """ + Convert maximal cliques across time from a list of NetworkX Graphs into an ASH. + + Each graph index is the start time of its clique hyperedges and node presence. + + :param graphs: Sequence of undirected NetworkX Graphs. + + :return: Time­sliced ASH with cliques as hyperedges. + """ + ash = ASH() + for t, graph in enumerate(graphs): + _validate_graph(graph) + for clique in nx.find_cliques(graph): + if len(clique) > 1: + ash.add_hyperedge(clique, start=t, end=t) + for node, data in graph.nodes(data=True): + ash.add_node( + node, start=t, end=t, attr_dict=NProfile(node, **copy.copy(data)) + ) + return ash + + +def from_networkx_bipartite( + graph: nx.Graph, + start: int, + end: Optional[int] = None, + keep_attrs: bool = False, +) -> ASH: + """ + Convert a bipartite NetworkX Graph into an ASH where one node set becomes hyperedges + and the other set becomes nodes. Edges connect hyperedges to their nodes. + + :param graph: Undirected bipartite NetworkX Graph. + :param start: Start time for presence. + :param end: Optional end time for presence. + :param keep_attrs: If True, preserves node attributes of the original graph. + + :raises ValueError: If the graph is not bipartite. + + :return: ASH with hyperedges corresponding to bipartite partitions. + """ + _validate_graph(graph) + if not nx.is_bipartite(graph): + raise ValueError("Provided Graph is not bipartite") + ash = ASH() + # collect nodes by partition + nodes, edges = nx.algorithms.bipartite.sets(graph) + # for each hyperedge (a node in one partition), take its neighbors + for he in edges: + neighbors = list(graph.neighbors(he)) + if neighbors: # only add non-empty hyperedges + print( + f"Adding hyperedge {he} with neighbors {neighbors} from graph {graph}" + ) + ash.add_hyperedge(neighbors, start=start, end=end) + # add all nodes + _add_nodes(ash, graph, start, end, keep_attrs, bipartite=True) + return ash + + +def from_networkx_bipartite_list( + graphs: Sequence[nx.Graph], + keep_attrs: bool = False, +) -> ASH: + """ + Time­sliced conversion of bipartite graphs into an ASH. + + :param graphs: Sequence of undirected bipartite NetworkX Graphs. + :param keep_attrs: If True, preserves node attributes. + + :return: ASH with hyperedges per snapshot. + """ + ash = ASH() + for t, graph in enumerate(graphs): + _validate_graph(graph) + if not nx.is_bipartite(graph): + raise ValueError(f"Graph at index {t} is not bipartite") + edges, nodes = nx.algorithms.bipartite.sets(graph) + # for each hyperedge (a node in one partition), take its neighbors + for he in edges: + neighbors = list(graph.neighbors(he)) + if neighbors: + ash.add_hyperedge(neighbors, start=t, end=t) + + node_data = ((node, graph.nodes[node]) for node in nodes) + + for node, data in node_data: + if keep_attrs: + attrs = copy.copy(data) + profile = NProfile(node, **attrs) + ash.add_node(node, start=t, end=t, attr_dict=profile) + else: + ash.add_node(node, start=t, end=t) + return ash diff --git a/ash_model/utils/profiles.py b/ash_model/utils/profiles.py new file mode 100644 index 0000000..74ac826 --- /dev/null +++ b/ash_model/utils/profiles.py @@ -0,0 +1,140 @@ +from collections import defaultdict +import numpy as np +from ash_model import ASH, NProfile + + +def aggregate_node_profile( + h: ASH, node: int, categorical_aggr: str = "mode", numerical_aggr: str = "mean" +) -> NProfile: + """ + Returns an aggregated profile of a node over all time points. + The categorical_aggr parameter specifies the aggregation method for categorical attributes. + The numerical_aggr parameter specifies the aggregation method for numerical attributes. + + :param h: The ASH object + :param node: The node id + :param categorical_aggr: The aggregation method for categorical attributes. Options: "mode", "first", "last" + :param numerical_aggr: The aggregation method for numerical attributes. Options: "mean", "median", "first", "last" + + :return: The aggregated profile of the node + """ + name_to_func = { + "mode": lambda x: max(set(x), key=x.count), + "first": lambda x: x[0], + "last": lambda x: x[-1], + "mean": lambda x: sum(x) / len(x), + "median": lambda x: sorted(x)[len(x) // 2], + } + + aggr_profile = NProfile(node) + attr_dicts = [ + h.get_node_profile(node, tid=t).get_attributes() + for t in sorted(h.node_presence(node)) + ] + attribute_values = defaultdict(list) + for attr_dict in attr_dicts: + for name, value in attr_dict.items(): + attribute_values[name].append(value) + + for name, values in attribute_values.items(): + if isinstance(values[0], str): + aggr_profile.add_attribute(name, name_to_func[categorical_aggr](values)) + else: + aggr_profile.add_attribute(name, name_to_func[numerical_aggr](values)) + return aggr_profile + + +def hyperedge_most_frequent_node_attribute_value( + h: ASH, hyperedge_id: str, attr_name: str, tid: int = None +) -> dict: + """ + Returns the most frequent value of a node attribute in a hyperedge. + If tid is specified, it returns the value at that time point. + If tid is None, it returns the most frequent value across all time points. + + :param h: The ASH object + :param hyperedge_id: The hyperedge id + :param attr_name: The attribute name to consider + :param tid: The temporal id. If None, considers all time points + + :return: A dictionary with the most frequent value of the attribute in the hyperedge nodes + """ + nodes = h.get_hyperedge_nodes(hyperedge_id) + values = [] + for node in nodes: + profile = h.get_node_profile(node, tid) + if profile.has_attribute(attr_name): + # If tid is specified, get the value at that time point + # If tid is None, it's the aggregated value across all time points + + values.append( + profile.get_attribute(attr_name) + if tid is not None + else profile.get_attribute(attr_name) + ) + + if not values: + return {} + + return { + max(set(values), key=values.count): values.count( + max(set(values), key=values.count) + ) + } + + +def hyperedge_aggregate_node_profile( + h: ASH, + hyperedge_id: str, + tid: int, + attr_name: str = None, + categorical_aggr: str = "mode", + numerical_aggr: str = "mean", +) -> NProfile: + """ + Returns an aggregated profile of the nodes in a hyperedge. + The categorical_aggr parameter specifies the aggregation method for categorical attributes. + The numerical_aggr parameter specifies the aggregation method for numerical attributes. + + :param h: The ASH object + :param hyperedge_id: The hyperedge id + :param tid: The temporal id + :param attr_name: The attribute name to aggregate. If None, all attributes are aggregated + :param categorical_aggr: The aggregation method for categorical attributes. Options: "mode", "first", "last" + :param numerical_aggr: The aggregation method for numerical attributes. Options: "mean", "median", "first", "last" + + :return: The aggregated profile of the hyperedge nodes + """ + name_to_func = { + "mode": lambda x: max(set(x), key=x.count), + "first": lambda x: x[0], + "last": lambda x: x[-1], + "mean": lambda x: sum(x) / len(x), + "median": lambda x: np.median(x), + } + + aggr_profile = NProfile(None) + nodes = h.get_hyperedge_nodes(hyperedge_id) + attribute_values = defaultdict(list) + for node in nodes: + profile = h.get_node_profile(node, tid) + + if not attr_name: + for name, value in profile.get_attributes().items(): + + attribute_values[name].append(value) + else: + attribute_values[attr_name].append(profile.get_attribute(attr_name)) + + for name, values in attribute_values.items(): + + if isinstance(values[0], str): + val = name_to_func[categorical_aggr](values) + aggr_profile.add_attribute(name, val) + + else: + val = name_to_func[numerical_aggr](values) + aggr_profile.add_attribute(name, val) + aggr_profile.add_statistic(name, "std", np.std(values)) + + return aggr_profile diff --git a/ash_model/utils/projections.py b/ash_model/utils/projections.py new file mode 100644 index 0000000..8ceab3d --- /dev/null +++ b/ash_model/utils/projections.py @@ -0,0 +1,270 @@ +import copy +from itertools import combinations +from typing import Dict, Optional +from collections import defaultdict + +import networkx as nx + +from ash_model import ASH, NProfile + + +def clique_projection( + h: ASH, + start: Optional[int] = None, + end: Optional[int] = None, + keep_attrs: bool = False, +) -> nx.Graph: + """ + Returns a NetworkX Graph object that is the clique projection of the + given ASH object. + The clique projection of a hypergraph is a graph constructed by placing + an edge between every pair of nodes that belong to the same hyperedge. + + :param h: The ASH object to be projected. + :param start: The start time of the projection (optional). + :param end: The end time of the projection (optional). + :param keep_attrs: If True, the attributes of the nodes in the ASH will + be preserved in the resulting NetworkX graph. + + :return: A NetworkX Graph object representing the clique projection of the ASH. + """ + + res = nx.Graph() + for edge in h.hyperedges(start=start, end=end, as_ids=False): + if len(edge) > 1: + for u, v in combinations(edge, 2): + if res.has_edge(u, v): + res[u][v]["weight"] += 1 + else: + res.add_edge(u, v, weight=1) + if keep_attrs: + for node in res.nodes(): + if node in h.nodes(): + # Copy attributes from ASH node to NetworkX node + attrs = h.get_node_attributes(node) + + res.nodes[node].update(attrs) + + return res + + +""" +Hypergraph projection functions. +""" + +from typing import Dict, Optional + +import networkx as nx + +from ash_model import ASH + + +def bipartite_projection( + h: ASH, + start: Optional[int] = None, + end: Optional[int] = None, + keep_attrs: bool = False, +) -> nx.Graph: + """ + Returns a NetworkX Graph object that is the bipartite projection of the + given ASH object. + The bipartite projection of a hypergraph is a graph constructed by placing + an edge between every node and every hyperedge that contains it. + + :param h: The ASH object to be projected. + :param start: The start time of the projection (optional). + :param end: The end time of the projection (optional). + :param keep_attrs: If True, the attributes of the nodes in the ASH will + be preserved in the resulting NetworkX graph. + + :return: A NetworkX Graph object representing the bipartite projection of the ASH. + """ + + hes = h.hyperedges(start, end) + + g = nx.Graph() + for he in hes: + g.add_node(he, bipartite=1) + nodes = h.get_hyperedge_nodes(he) + for node in nodes: + if not g.has_node(node): + g.add_node(node, bipartite=0) + g.add_edge(node, he) + if keep_attrs: + for node in g.nodes(): + if node in h.nodes(): + # Copy attributes from ASH node to NetworkX node + attrs = h.get_node_attributes(node) + g.nodes[node].update(attrs) + return g + + +def line_graph_projection( + h: ASH, + s: int = 1, + start: Optional[int] = None, + end: Optional[int] = None, + keep_attrs: bool = False, +) -> nx.Graph: + """ + Returns a NetworkX Graph object that is the line graph projection of the + given ASH object. + The line graph projection of a hypergraph is a graph constructed by placing + an edge between every pair of hyperedges that share at least one node. + + :param h: The ASH object to be projected. + :param s: The size of the edge overlap. + :param end: The end time of the projection (optional). + :param keep_attrs: If True, the attributes of the nodes in the ASH will + be preserved in the resulting NetworkX graph. + + :return: A NetworkX Graph object representing the line graph projection of the ASH. + """ + + g = nx.Graph() + + # Get hyperedges in the specified time window that have at least s nodes + hyperedges = [ + he for he in h.hyperedges(start, end) if len(h.get_hyperedge_nodes(he)) >= s + ] + + if keep_attrs: + for he in hyperedges: + g.add_node(he, attr_dict=h.hyperedges[he].attr_dict.to_dict()) + else: + for he in hyperedges: + g.add_node(he) + + # Add edges between hyperedges that intersect in at least s nodes + for i, he1 in enumerate(hyperedges): + for he2 in hyperedges[i + 1 :]: + nodes1 = set(h.get_hyperedge_nodes(he1)) + nodes2 = set(h.get_hyperedge_nodes(he2)) + intersection_size = len(nodes1 & nodes2) + + if intersection_size >= s: + g.add_edge(he1, he2, w=intersection_size) + + return g + + +def dual_hypergraph_projection( + h: ASH, start: Optional[int] = None, end: Optional[int] = None +) -> tuple: + """ + The dual_hypergraph function takes a hypergraph and returns the dual of that hypergraph. + The dual of a hypergraph is a hypergraph where each hyperedge becomes a node, and each + node is connected to every other node in its corresponding hyperedge. The function also + returns a node-to-edge mapping dictionary that maps each node in the original hypergraph + to the new hyperedge ids in the dual hypergraph. + + :param h: The ASH object to be transformed into a dual hypergraph. + :param start: Specify the start of a time window + :param end: SpSpecify the end of a time window + + :return: the dual ASH and a node-to-edge mapping dictionary + """ + + b = ASH() + node_to_edges = defaultdict(list) + for he in h.hyperedges(start, end): + nodes = h.get_hyperedge_nodes(he) + for node in nodes: + node_to_edges[node].append(he) + + old_nodes_to_new_edges = {} + for node, edges in node_to_edges.items(): + b.add_hyperedge(edges, start=0, end=None) + eid = b.get_hyperedge_id(edges) + old_nodes_to_new_edges[node] = eid + + return b, old_nodes_to_new_edges + + +def clique_projection_by_time(h: ASH, keep_attrs: bool = False) -> Dict[int, nx.Graph]: + """ + Returns a dictionary of NetworkX Graph objects that are the clique projections + of the given ASH object for each time step. + + :param h: The ASH object to be projected. + :param keep_attrs: If True, the attributes of the nodes in the ASH will + be preserved in the resulting NetworkX graphs. + + :return: A dictionary where keys are time steps and values are NetworkX Graph objects + representing the clique projection of the ASH at that time step. + """ + + clique_projections = {} + for t in h.temporal_snapshots_ids(): + clique_projections[t] = clique_projection( + h, start=t, end=t, keep_attrs=keep_attrs + ) + + return clique_projections + + +def bipartite_projection_by_time( + h: ASH, keep_attrs: bool = False +) -> Dict[int, nx.Graph]: + """ + Returns a dictionary of NetworkX Graph objects that are the bipartite projections + of the given ASH object for each time step. + + :param h: The ASH object to be projected. + :param keep_attrs: If True, the attributes of the nodes in the ASH will + be preserved in the resulting NetworkX graphs. + + :return: A dictionary where keys are time steps and values are NetworkX Graph objects + representing the bipartite projection of the ASH at that time step. + """ + + bipartite_projections = {} + for t in h.temporal_snapshots_ids(): + bipartite_projections[t] = bipartite_projection( + h, start=t, end=t, keep_attrs=keep_attrs + ) + + return bipartite_projections + + +def line_graph_projection_by_time( + h: ASH, s: int = 1, keep_attrs: bool = False +) -> Dict[int, nx.Graph]: + """ + Returns a dictionary of NetworkX Graph objects that are the line graph projections + of the given ASH object for each time step. + + :param h: The ASH object to be projected. + :param s: The size of the edge overlap. + :param keep_attrs: If True, the attributes of the nodes in the ASH will + be preserved in the resulting NetworkX graphs. + + :return: A dictionary where keys are time steps and values are NetworkX Graph objects + representing the line graph projection of the ASH at that time step. + """ + + line_graph_projections = {} + for t in h.temporal_snapshots_ids(): + line_graph_projections[t] = line_graph_projection( + h, s=s, start=t, end=t, keep_attrs=keep_attrs + ) + + return line_graph_projections + + +def dual_hypergraph_projection_by_time(h: ASH) -> Dict[int, tuple]: + """ + Returns a dictionary of dual hypergraphs for each time step in the ASH object. + Each entry in the dictionary contains the dual ASH and a node-to-edge mapping dictionary. + + :param h: The ASH object to be transformed into dual hypergraphs. + + :return: A dictionary where keys are time steps and values are tuples containing + the dual ASH and a node-to-edge mapping dictionary. + """ + + dual_hypergraphs = {} + for t in h.temporal_snapshots_ids(): + dual_hypergraphs[t] = dual_hypergraph_projection(h, start=t, end=t) + + return dual_hypergraphs diff --git a/ash_model/utils/undirected_graph_transformations.py b/ash_model/utils/undirected_graph_transformations.py deleted file mode 100644 index b50b9a7..0000000 --- a/ash_model/utils/undirected_graph_transformations.py +++ /dev/null @@ -1,131 +0,0 @@ -import copy - -import networkx as nx - -from ash_model import ASH, NProfile - - -def to_graph_decomposition(H: ASH, tid: int = None) -> dict: - """Returns an ASH object that has the same nodes (and - corresponding attributes) as the given H, except that for all - hyperedges in the given H, each node in the hyperedge is pairwise - connected to every other node also in that hyperedge in the new H. - Said another way, each of the original hyperedges are decomposed in the - new H into cliques (aka the "2-section" or "clique graph"). - :param H: the H to decompose into a graph. - :param tid: - :returns: ASH -- the decomposed H. - :raises: TypeError -- Transformation only applicable to - undirected Hs - """ - if not isinstance(H, ASH): - raise TypeError( - "Transformation only applicable to \ - undirected Hs" - ) - - if tid is not None: - tids = [tid] - else: - tids = H.snapshots.keys() - - res = {} - - for tid in tids: - G = ASH() - - for node in H.node_iterator(tid=tid): - profile = H.get_node_profile(node, tid=tid) - G.add_node(node, start=tid, attr_dict=profile) - - edges = [ - (node_a, node_b) - for hyperedge_id in H.hyperedge_id_iterator(start=tid) - for node_a in H.get_hyperedge_nodes(hyperedge_id) - for node_b in H.get_hyperedge_nodes(hyperedge_id) - if node_a != node_b - ] - - G.add_hyperedges(edges, start=tid) - res[tid] = G - - return res - - -def to_networkx_graph(H: ASH, tid: int = None) -> dict: - """Returns a NetworkX Graph object that is the graph decomposition of - the given H. - See "to_graph_decomposition()" for more details. - :param H: the H to decompose into a graph. - :param tid: - :returns: nx.Graph -- NetworkX Graph object representing the - decomposed H. - :raises: TypeError -- Transformation only applicable to - undirected Hs - """ - - if not isinstance(H, ASH): - raise TypeError( - "Transformation only applicable to \ - undirected Hs" - ) - - if tid is not None: - tids = [tid] - else: - tids = H.snapshots.keys() - - res = {} - - for tid in tids: - G = to_graph_decomposition(H, tid)[tid] - - nx_graph = nx.Graph() - - for node in G.node_iterator(): - nx_graph.add_node( - node, **G.get_node_profile(node, tid=tid).get_attributes() - ) - - for hyperedge_id in G.hyperedge_id_iterator(): - edge_nodes = G.get_hyperedge_nodes(hyperedge_id) - edge_attributes = G.get_hyperedge_attributes(hyperedge_id) - nx_graph.add_edge(edge_nodes[0], edge_nodes[1], **edge_attributes) - - res[tid] = nx_graph - - return res - - -def from_networkx_graph(nx_graph: nx.Graph, start: int, end: int = None) -> ASH: - """Returns an UndirectedHypergraph object that is the graph equivalent of - the given NetworkX Graph object. - :param nx_graph: the NetworkX undirected graph object to transform. - :param start: - :param end: - :returns: UndirectedHypergraph -- H object equivalent to the - NetworkX undirected graph. - :raises: TypeError -- Transformation only applicable to undirected - NetworkX graphs - """ - - if not isinstance(nx_graph, nx.Graph): - raise TypeError( - "Transformation only applicable to undirected \ - NetworkX graphs" - ) - - G = ASH(hedge_removal=True) - - for node in nx_graph.nodes(): - G.add_node( - node, - start=start, - end=end, - attr_dict=NProfile(node, **copy.copy(nx_graph.nodes[node])), - ) - - for edge in nx_graph.edges(): - G.add_hyperedge([edge[0], edge[1]], start=start, end=end) - - return G diff --git a/ash_model/utils/undirected_matrices.py b/ash_model/utils/undirected_matrices.py deleted file mode 100644 index d24b598..0000000 --- a/ash_model/utils/undirected_matrices.py +++ /dev/null @@ -1,134 +0,0 @@ -import halp.utilities.undirected_matrices as um -import numpy as np -from scipy import sparse - -from ash_model import ASH - - -def get_node_mapping(h: ASH) -> (dict, dict): - """ - - :param h: - :param tid: - :return: - """ - return um.get_node_mapping(h.H) - - -def get_hyperedge_id_mapping(h: ASH) -> (dict, dict): - """ - - :param h: - :return: - """ - return um.get_hyperedge_id_mapping(h.H) - - -def get_incidence_matrix( - h: ASH, nodes_to_indices: dict, hyperedge_ids_to_indices: dict, tid: int = None -) -> dict: - """ - - :param h: - :param tid: - :param nodes_to_indices: - :param hyperedge_ids_to_indices: - :return: - """ - - if tid is not None: - tids = [tid] - else: - tids = h.snapshots - - res = {} - for tid in tids: - h1, old_to_new = h.hypergraph_temporal_slice(tid) - s = h1.H - - rows, cols = [], [] - for hyperedge_id, hyperedge_index in hyperedge_ids_to_indices.items(): - try: - for node in s.get_hyperedge_nodes(hyperedge_id): - # get the mapping between the node and its ID - rows.append(nodes_to_indices.get(node)) - cols.append(hyperedge_index) - except: - pass - - values = np.ones(len(rows), dtype=int) - node_count = len(nodes_to_indices) - hyperedge_count = len(hyperedge_ids_to_indices) - - res[tid] = sparse.csc_matrix( - (values, (rows, cols)), shape=(node_count, hyperedge_count) - ) - - return res - - -def get_hyperedge_weight_matrix( - h: ASH, hyperedge_ids_to_indices: dict, tid: int = None -) -> dict: - """ - - :param h: - :param nodes_to_indices: - :param hyperedge_ids_to_indices: - :param tid: - :return: - """ - if tid is not None: - tids = [tid] - else: - tids = h.snapshots - - res = {} - for tid in tids: - hyperedge_weights = {} - for hyperedge_id in h.hyperedge_id_iterator(): - hyperedge_weights.update( - { - hyperedge_ids_to_indices[hyperedge_id]: h.get_hyperedge_weight( - hyperedge_id - ) - } - ) - - hyperedge_weight_vector = [] - for i in range(len(hyperedge_weights.keys())): - hyperedge_weight_vector.append(hyperedge_weights.get(i)) - - res[tid] = sparse.diags([hyperedge_weight_vector], [0]) - - return res - - -def get_vertex_degree_matrix(h: ASH, tid: int = None) -> dict: - """ - - :param h: - :param tid: - :return: - """ - - if tid is not None: - tids = [tid] - else: - tids = h.snapshots - - res = {} - for tid in tids: - _, node_to_index = get_node_mapping(h) - _, edge_to_index = get_hyperedge_id_mapping(h) - W = get_hyperedge_weight_matrix( - h, hyperedge_ids_to_indices=edge_to_index, tid=tid - )[tid] - M = get_incidence_matrix( - h, - nodes_to_indices=node_to_index, - hyperedge_ids_to_indices=edge_to_index, - tid=tid, - )[tid] - res[tid] = um.get_vertex_degree_matrix(M, W) - return res diff --git a/ash_model/viz/__init__.py b/ash_model/viz/__init__.py index 690bf62..449bd31 100644 --- a/ash_model/viz/__init__.py +++ b/ash_model/viz/__init__.py @@ -1,2 +1,2 @@ -from .temporal import * from .static import * +from .temporal import * diff --git a/ash_model/viz/static.py b/ash_model/viz/static.py index 7e21145..0a3c69e 100644 --- a/ash_model/viz/static.py +++ b/ash_model/viz/static.py @@ -5,15 +5,16 @@ def plot_s_degrees(h: ASH, smax: int, loglog: bool = True, **kwargs: object) -> object: """ - The plot_s_degrees function plots the s-degree distribution of a hypergraph. - A line for each s will be plotted, from 1 to :smax: inclusive. - Matplotlib plotting parameters (e.g., color) can be passed as **kwargs. + Plot the s-degree distribution of a hypergraph. + + A line for each s will be plotted, from 1 to smax inclusive. + Matplotlib plotting parameters (e.g., color) can be passed as kwargs. :param h: ASH instance - :param smax: Set the maximum value of s - :param loglog: Specify whether the plot should be loglog or not - :param kwargs: Pass matplotlib keyword arguments to the function - :return: The axes object + :param smax: Maximum value of s + :param loglog: If True, plot in log-log scale + :param kwargs: Matplotlib keyword arguments (e.g., ax, color, linewidth) + :return: The matplotlib axes object """ if "ax" not in kwargs: @@ -21,12 +22,12 @@ def plot_s_degrees(h: ASH, smax: int, loglog: bool = True, **kwargs: object) -> else: ax = kwargs["ax"] - nodes = h.get_node_set() + nodes = h.nodes() ss = np.arange(1, smax + 1, 1) degs = {s: {n: 0 for n in nodes} for s in ss} for n in nodes: for s in ss: - degs[s][n] = h.get_s_degree(n, s) + degs[s][n] = h.s_degree(n, s) for s in ss: deg = dict(sorted(degs[s].items(), key=lambda item: item[1], reverse=True)) @@ -51,15 +52,16 @@ def plot_hyperedge_size_distribution( h: ASH, max_size: int = None, min_size: int = None, **kwargs: object ) -> object: """ - The plot_hyperedge_size_distribution function plots the distribution of hyperedge sizes in a hypergraph. - :min_size: and :max_size: can be used to filter out hyperedges. - Matplotlib plotting parameters (e.g., color) can be passed as **kwargs. + Plot the distribution of hyperedge sizes in a hypergraph. + + min_size and max_size can be used to filter out hyperedges. + Matplotlib plotting parameters (e.g., color) can be passed as kwargs. :param h: ASH instance - :param max_size: Specify the maximum size of hyperedges to be plotted - :param min_size: Specify the minimum size of hyperedges to be plotted - :param kwargs: Pass matplotlib keyword arguments to the function - :return: The axes object + :param max_size: Maximum size of hyperedges to be plotted (optional) + :param min_size: Minimum size of hyperedges to be plotted (optional) + :param kwargs: Matplotlib keyword arguments (e.g., ax, color, alpha) + :return: The matplotlib axes object """ if "ax" not in kwargs: @@ -80,24 +82,25 @@ def plot_hyperedge_size_distribution( def plot_degree_distribution(h: ASH, loglog: bool = True, **kwargs: object) -> object: """ - The plot_degree_distribution function plots the degree distribution of an ASH. + Plot the degree distribution of an ASH hypergraph. + The default is to draw a log-log plot. - Matplotlib plotting parameters (e.g., color) can be passed as **kwargs. + Matplotlib plotting parameters (e.g., color) can be passed as kwargs. :param h: ASH instance - :param loglog: Whether to plot the degree distribution in log-log scale - :param kwargs: Pass matplotlib keyword arguments to the function - :return: The axes object + :param loglog: If True, plot in log-log scale + :param kwargs: Matplotlib keyword arguments (e.g., ax, color, alpha) + :return: The matplotlib axes object """ if "ax" not in kwargs: ax = plt.gca() else: ax = kwargs["ax"] - nodes = h.get_node_set() + nodes = h.nodes() degs = {n: 0 for n in nodes} for n in nodes: - degs[n] = h.get_degree(n) + degs[n] = h.degree(n) deg = dict(sorted(degs.items(), key=lambda item: item[1], reverse=True)) y = list(deg.values()) @@ -111,27 +114,28 @@ def plot_degree_distribution(h: ASH, loglog: bool = True, **kwargs: object) -> o def plot_s_ranks(h: ASH, smax: int, loglog: bool = True, **kwargs: object) -> object: """ - The plot_s_ranks function plots the s-degree distribution of a hypergraph. - A line for each s will be plotted, from 1 to :smax: inclusive. - Matplotlib plotting parameters (e.g., color) can be passed as **kwargs. + Plot the s-degree rank distribution of a hypergraph. + + A line for each s will be plotted, from 1 to smax inclusive. + Matplotlib plotting parameters (e.g., color) can be passed as kwargs. :param h: ASH instance - :param smax: Set the maximum value of s - :param loglog: Specify whether the plot should be loglog or not - :param kwargs: Pass matplotlib keyword arguments to the function - :return: The axes object + :param smax: Maximum value of s + :param loglog: If True, plot in log-log scale + :param kwargs: Matplotlib keyword arguments (e.g., ax, color, label) + :return: The matplotlib axes object """ if "ax" not in kwargs: ax = plt.gca() else: ax = kwargs["ax"] - nodes = h.get_node_set() + nodes = h.nodes() ss = np.arange(1, smax + 1, 1) degs = {s: {n: 0 for n in nodes} for s in ss} for n in nodes: for s in ss: - degs[s][n] = h.get_s_degree(n, s) + degs[s][n] = h.s_degree(n, s) for s in ss: deg = dict(sorted(degs[s].items(), key=lambda item: item[1], reverse=True)) diff --git a/ash_model/viz/temporal.py b/ash_model/viz/temporal.py index 502d9ea..3780bdf 100644 --- a/ash_model/viz/temporal.py +++ b/ash_model/viz/temporal.py @@ -1,160 +1,259 @@ -import matplotlib.pyplot as plt -import pandas as pd -import seaborn as sns +from __future__ import annotations -from ash_model.measures import * +from typing import Iterable, List, Optional, Sequence +import matplotlib.pyplot as plt +import numpy as np -def __rolling_mean(it, window): - """ +from ash_model.classes import ASH # type: ignore - :param it: - :param window: - :return: - """ - return pd.Series(it).rolling(window=window).mean() +__all__ = [ + "plot_hyperedge_activity_series", + "plot_node_activity_series", + "plot_presence_timeline", + "plot_inter_event_time_distribution", + "plot_hyperedge_lifespan_distribution", + "plot_node_lifespan_distribution", +] -def plot_structure_dynamics( - h: ASH, func: Callable, func_params: dict = None, rolling: int = None, **kwargs -) -> object: - """ +# --------------------------------------------------------------------------- +# Helper utilities (internal) +# --------------------------------------------------------------------------- - :param h: ASH instance - :param func: function to be called at each timestamp - :param func_params: parameters of the above function in key-value pairs - :param rolling: size of the rolling window - :param kwargs: Pass matplotlib keyword arguments to the function - :return: The axes object - """ - if func_params is None: - func_params = {} - if "h" in func.__code__.co_varnames: # e.g., inclusiveness - func_params.update({"h": h}) +def _get_ax(kwargs): + if "ax" in kwargs and kwargs["ax"] is not None: + return kwargs["ax"] + return plt.gca() - if "tid" in func.__code__.co_varnames: - y = [ - func(**func_params, tid=tid) for tid in h.temporal_snapshots_ids() - ] # e.g., inclusiveness - else: # has 'start' and 'end', e.g. average_s_local_clustering_coefficient - y = [ - func(**func_params, start=tid, end=tid) - for tid in h.temporal_snapshots_ids() - ] +# --------------------------------------------------------------------------- +# Public plotting helpers +# --------------------------------------------------------------------------- - if rolling: - y = __rolling_mean(y, window=rolling) - if "ax" not in kwargs: - ax = plt.gca() - else: - ax = kwargs["ax"] +def plot_hyperedge_activity_series(h: ASH, normalize: bool = False, **kwargs): + """Plot the number of active hyperedges at each temporal snapshot. - ax.plot(y, **{k: v for k, v in kwargs.items() if k != "ax"}) + :param h: ASH instance. + :param normalize: If True divide activity by the maximum (y in [0,1]). + :param kwargs: Matplotlib customisation (``color``, ``ax`` …). + :return: Matplotlib Axes with the line plot. + """ + ax = _get_ax(kwargs) + tids = h.temporal_snapshots_ids() + if not tids: + return ax + activity = [h.number_of_hyperedges(t) for t in tids] + if normalize and any(activity): + m = max(activity) + activity = [a / m for a in activity] + ax.plot( + tids, + activity, + marker="o", + linewidth=1, + ms=3, + **{k: v for k, v in kwargs.items() if k != "ax"}, + ) + ax.set_xlabel("Time") + ax.set_ylabel("Activity" + (" (normalized)" if normalize else "")) + ax.set_title("Hyperedge activity over time") return ax -def plot_attribute_dynamics( +# --------------------------------------------------------------------------- +# Backward-compat aliases (kept for older tests/examples) +# --------------------------------------------------------------------------- + + +def plot_node_activity_series( h: ASH, - attr_name: str, - func: Callable, - func_params: dict = None, - rolling: int = None, - **kwargs -) -> object: - """ + *, + normalize: bool = False, + **kwargs, +): + """Plot the activity over time for selected nodes. - :param h: ASH instance - :param attr_name: attribute name - :param func: function to be called at each timestamp - :param func_params: parameters of the above function in key-value pairs - :param rolling: size of the rolling window - :param kwargs: Pass matplotlib keyword arguments to the function - :return: The axes object + :param h: ASH instance. + :param normalize: If True divide node's activity by its maximum (y in [0,1]). + :param kwargs: Matplotlib customisation (``color``, ``ax`` …). + :return: Matplotlib Axes with the line plot. """ - if func_params is None: - func_params = {} - if "h" in func.__code__.co_varnames: # e.g., inclusiveness - func_params.update({"h": h}) + ax = _get_ax(kwargs) + tids = h.temporal_snapshots_ids() + if not tids: + return ax + + activity = [h.number_of_nodes(t) for t in tids] + if normalize and any(activity): + m = max(activity) + activity = [a / m for a in activity] + ax.plot( + tids, + activity, + marker="o", + linewidth=1, + ms=3, + **{k: v for k, v in kwargs.items() if k != "ax"}, + ) + + ax.set_xlabel("Time") + ax.set_ylabel("Activity" + (" (normalized)" if normalize else "")) + ax.set_title("Node activity over time") + ax.legend() + return ax + - res = defaultdict(list) +def plot_presence_timeline( + h: ASH, + *, + hyperedges: Optional[Iterable[int]] = None, + nodes: Optional[Iterable[int]] = None, + **kwargs, +): + """Plot a presence timeline (Gantt‑like) for given hyperedges or nodes. - for tid in h.temporal_snapshots_ids(): - res_t = func(**func_params, tid=tid)[attr_name] - if isinstance(res_t, dict): # if result is by label - for label in res_t: - res[label].append(res_t[label]) - else: # if result is aggregated - res[attr_name].append(res_t) + One of ``hyperedges`` or ``nodes`` must be provided. If both are + provided, ``hyperedges`` takes precedence. + + :param h: ASH instance. + :param hyperedges: Iterable of hyperedge IDs to plot. + :param nodes: Iterable of node IDs to plot. + :param kwargs: Matplotlib customisation (``color``, ``ax`` …). + :return: Matplotlib Axes with the timeline plot. + """ - if "ax" not in kwargs: - ax = plt.gca() + ax = _get_ax(kwargs) + if hyperedges is not None: + items = list(hyperedges) + presences = [ + (hid, h.hyperedge_presence(hid)) + for hid in items + if h.hyperedge_presence(hid) + ] + item_type = "Hyperedge" + elif nodes is not None: + items = list(nodes) + presences = [ + (nid, h.node_presence(nid)) for nid in items if h.node_presence(nid) + ] + item_type = "Node" else: - ax = kwargs["ax"] + raise ValueError("One of 'hyperedges' or 'nodes' must be provided.") - for name, y in res.items(): - if rolling: - y = __rolling_mean(y, window=rolling) - ax.plot(y, label=name, **{k: v for k, v in kwargs.items() if k != "ax"}) - ax.legend() + if not presences: + return ax + + for i, (item_id, times) in enumerate(presences): + ax.vlines( + times, + i + 0.5, + i + 1.5, + linewidth=4, + **{k: v for k, v in kwargs.items() if k != "ax"}, + ) + + ax.set_yticks(np.arange(1, len(presences) + 1)) + ax.set_yticklabels([str(item_id) for item_id, _ in presences]) + ax.set_xlabel("Time") + ax.set_ylabel(item_type + " ID") + ax.set_title(f"{item_type} presence timeline") return ax -# def plot_temporal_attribute_distribution(h, attr_name, **kwargs): -# -# if 'ax' not in kwargs: -# ax = plt.gca() -# tids = h.temporal_snapshots_ids() -# -# labels = h.node_attributes_to_attribute_values()[attr_name] -# -# distr = {label: {t: 0 for t in tids} for label in labels} -# -# for t in tids: -# nodes = h.get_node_set(tid=t) -# node_count = 0 -# for node in nodes: -# prof = h.get_node_profile(node, t) -# attr = prof.get_attribute(attr_name) -# distr[attr][t] += 1 -# node_count += 1 -# -# for label in labels: -# distr[label][t] = distr[label][t] / node_count -# data = pd.DataFrame(distr, columns=sorted(distr.keys())).transpose() -# sns.heatmap(data=data, ax=ax, **kwargs) -# -# return ax - - -def plot_consistency(h, **kwargs): +def plot_inter_event_time_distribution(h: ASH, **kwargs): + """Plot distribution of inter‑event times for hyperedge activations. + + We define an activation as a ``+`` event produced by + ``ASH.stream_interactions``. Inter‑event gaps are differences between + consecutive activation times (across all hyperedges). + + :param h: ASH instance. + :param kwargs: Matplotlib bar customisation (``color``, ``ax`` …). + :return: Axes """ - Plot the kde of the distribution of the consistency values for all nodes in the ASH. - Given a node and an attribute, the node's consistency w.r.t. the attribute is the complementary of the entropy - computed on the set of the attribute's values the node holds in time. - :param h: ASH instance - :param kwargs: Pass matplotlib keyword arguments to the function - :return: The axes object + ax = _get_ax(kwargs) + events = [t for (t, _hid, et) in h.stream_interactions() if et == "+"] + if len(events) < 2: + return ax + events = sorted(events) + diffs = np.diff(events) + unique, counts = np.unique(diffs, return_counts=True) + ax.bar( + unique, + counts, + width=0.8, + alpha=0.6, + **{k: v for k, v in kwargs.items() if k != "ax"}, + ) + ax.set_xlabel("Inter‑event time Δt") + ax.set_ylabel("Count") + ax.set_title("Inter‑event time distribution") + return ax + + +def plot_hyperedge_lifespan_distribution(h: ASH, **kwargs): + """Histogram of hyperedge lifespans (duration in snapshots). + + For each hyperedge we compute ``(last_presence - first_presence + 1)``. + + :param h: ASH instance. + :param kwargs: Matplotlib customisation (``bins``, ``color``, ``ax`` …). + :return: Axes """ - if "ax" not in kwargs: - ax = plt.gca() - else: - ax = kwargs["ax"] + ax = _get_ax(kwargs) + lifespans: List[int] = [] + for hid in h.hyperedges() if hasattr(h, "hyperedges") else []: # fallback safety + pres = h.hyperedge_presence(hid) if hasattr(h, "hyperedge_presence") else [] + if pres: + lifespans.append(max(pres) - min(pres) + 1) + if not lifespans: + return ax + bins = kwargs.get("bins", min(30, len(set(lifespans)))) + ax.hist( + lifespans, + bins=bins, + alpha=0.6, + **{k: v for k, v in kwargs.items() if k not in {"ax", "bins"}}, + ) + ax.set_xlabel("Lifespan (snapshots)") + ax.set_ylabel("#Hyperedges") + ax.set_title("Hyperedge lifespan distribution") + return ax - cons = consistency(h) - for attr_name in list(cons.values())[0]: - y = [v[attr_name] for v in cons.values()] - sns.kdeplot( - y, label=attr_name, ax=ax, **{k: v for k, v in kwargs.items() if k != "ax"} - ) - ax.legend() - ax.set_xlim((-0.2, 1.2)) +def plot_node_lifespan_distribution(h: ASH, **kwargs): + """Histogram of node lifespans (duration in snapshots). + + For each node we compute ``(last_presence - first_presence + 1)``. + + :param h: ASH instance. + :param kwargs: Matplotlib customisation (``bins``, ``color``, ``ax`` …). + :return: Axes + """ + ax = _get_ax(kwargs) + lifespans: List[int] = [] + for nid in h.nodes() if hasattr(h, "nodes") else []: # fallback safety + pres = h.node_presence(nid) if hasattr(h, "node_presence") else [] + if pres: + lifespans.append(max(pres) - min(pres) + 1) + if not lifespans: + return ax + bins = kwargs.get("bins", min(30, len(set(lifespans)))) + ax.hist( + lifespans, + bins=bins, + alpha=0.6, + **{k: v for k, v in kwargs.items() if k not in {"ax", "bins"}}, + ) + ax.set_xlabel("Lifespan (snapshots)") + ax.set_ylabel("#Nodes") + ax.set_title("Node lifespan distribution") return ax diff --git a/conda/build.sh b/conda/build.sh new file mode 100644 index 0000000..a660906 --- /dev/null +++ b/conda/build.sh @@ -0,0 +1 @@ +$PYTHON setup.py install --single-version-externally-managed --record=record.txt diff --git a/conda/conda_build_config.yaml b/conda/conda_build_config.yaml new file mode 100644 index 0000000..1c8c554 --- /dev/null +++ b/conda/conda_build_config.yaml @@ -0,0 +1,2 @@ +python: +- 3.9 diff --git a/conda/meta.yaml b/conda/meta.yaml new file mode 100644 index 0000000..2d86fbe --- /dev/null +++ b/conda/meta.yaml @@ -0,0 +1,33 @@ +package: + name: "ash" + version: "0.1.0" + +source: + git_rev: v0.1.0 + git_url: https://github.com/GiulioRossetti/ASH + +requirements: + host: + - python + - setuptools + build: + - python + - setuptools + run: + - python>=3.9 + - numpy + - halp + - scipy + - networkx + - tqdm + +about: + home: https://github.com/GiulioRossetti/ASH + license: BSD-2-Clause + license_familY: BSD + license_file: LICENSE + summary: "Attributed Stream Hypergraph library" + +extra: + recipe-maintainers: + - GiulioRossetti diff --git a/docs/Makefile b/docs/Makefile old mode 100644 new mode 100755 diff --git a/docs/_static/ash.png b/docs/_static/ash.png new file mode 100755 index 0000000..cdb798f Binary files /dev/null and b/docs/_static/ash.png differ diff --git a/docs/_static/css/custom.css b/docs/_static/css/custom.css old mode 100644 new mode 100755 diff --git a/docs/conf.py b/docs/conf.py old mode 100644 new mode 100755 index 7ed81ce..a8ec0d1 --- a/docs/conf.py +++ b/docs/conf.py @@ -12,42 +12,46 @@ # import os import sys +from pathlib import Path -import sphinx_rtd_theme +# Ensure pandoc is in PATH for nbsphinx +try: + import pypandoc + + pandoc_dir = str(Path(pypandoc.get_pandoc_path()).parent) + if pandoc_dir not in os.environ.get("PATH", ""): + os.environ["PATH"] = f"{pandoc_dir}{os.pathsep}{os.environ.get('PATH', '')}" +except ImportError: + pass # pypandoc not available, assume system pandoc -sys.path.append(os.path.join(os.path.dirname(__file__), "..")) +ROOT = Path(__file__).resolve().parents[1] +sys.path.insert(0, str(ROOT)) try: from ash_model import __version__ except ImportError: - __version__ = u'0.1.0' + __version__ = "1.0.0" -html_theme = "sphinx_rtd_theme" -html_theme_path = [sphinx_rtd_theme.get_html_theme_path()] +html_theme = "furo" version = __version__ # The full version, including alpha/beta/rc tags. release = version html_theme_options = { - "collapse_navigation": False, - "display_version": False, - "navigation_depth": 3, + "light_logo": "ash.png", + "dark_logo": "ash.png", } # -- Project information ----------------------------------------------------- project = "ASH" -copyright = "2024, Giulio Rossetti" +copyright = "2025, Giulio Rossetti" author = "Giulio Rossetti, Andrea Failla, Salvatore Citraro" autodoc_mock_imports = [ - "numpy", - "halp.undirected_hypergraph", - "halp.utilities.undirected_matrices", + "numpy", "matplotlib.pyplot", - "ash_model" "math", - "halp", "matplotlib", "networkx", "seaborn", @@ -55,6 +59,7 @@ "tqdm", "seaborn", "pandas", + "csrgraph", ] # -- General configuration --------------------------------------------------- @@ -67,8 +72,31 @@ "sphinx.ext.githubpages", "sphinx.ext.autodoc", "sphinx.ext.autosummary", + "sphinx.ext.viewcode", + "sphinx.ext.napoleon", # supporto Google/NumPy style docstrings + "sphinx.ext.intersphinx", # cross-link con altra doc + "nbsphinx", # Jupyter notebook support ] +# Make autosummary scan pages and create stubs automatically +autosummary_generate = True # Abilitato per generare tabelle riepilogo API +autosummary_generate_overwrite = False +napoleon_google_docstring = True +napoleon_numpy_docstring = True +napoleon_include_init_with_doc = True +napoleon_use_rtype = True +napoleon_preprocess_types = True + +# Mostra i type hints nella signature e non duplicati nella descrizione +autodoc_typehints = "description" +autodoc_typehints_format = "short" + +autodoc_default_options = { + "members": True, + "undoc-members": False, + "inherited-members": True, +} + # Add any paths that contain templates here, relative to this directory. templates_path = ["_templates"] @@ -76,7 +104,68 @@ # List of patterns, relative to source directory, that match files and # directories to ignore when looking for source files. # This pattern also affects html_static_path and html_extra_path. -exclude_patterns = ["_build", "Thumbs.db", ".DS_Store"] +exclude_patterns = [ + "_build", + "Thumbs.db", + ".DS_Store", + "**.ipynb_checkpoints", +] + +# Intersphinx mapping per link esterni +intersphinx_mapping = { + "python": ("https://docs.python.org/3", None), + "numpy": ("https://numpy.org/doc/stable/", None), + "networkx": ("https://networkx.org/documentation/stable/", None), + "matplotlib": ("https://matplotlib.org/stable/", None), + "scipy": ("https://docs.scipy.org/doc/scipy/", None), + "pandas": ("https://pandas.pydata.org/pandas-docs/stable/", None), +} + +# Opzioni per ordina membri (mantiene ordine sorgente) +autodoc_member_order = "bysource" + +# Evita warning se mancano __all__ +autodoc_inherit_docstrings = True + +# -- nbsphinx configuration -------------------------------------------------- + +# Add the tutorial directory to the source paths +import shutil + +tutorial_source = ROOT / "tutorial" +tutorial_dest = Path(__file__).parent / "tutorial" + +# Create symlink or copy notebooks to docs/tutorial if they don't exist +if not tutorial_dest.exists(): + tutorial_dest.mkdir(exist_ok=True) + +# This is processed by Jinja2 and inserted before each notebook +nbsphinx_prolog = r""" +{% set docname = env.doc2path(env.docname, base=None) %} + +.. raw:: html + +
+

Note

+

This page was generated from + {{ docname|e }}. +

+
+""" + +# Execute notebooks before conversion: 'always', 'never', 'auto' (default) +nbsphinx_execute = ( + "never" # Don't execute notebooks during build (they should be pre-executed) +) + +# Allow errors in notebook execution +nbsphinx_allow_errors = True + +# Timeout for notebook execution (in seconds) +nbsphinx_timeout = 180 + +# Exclude output files and checkpoint folders +nbsphinx_exclude_output_prompt = False # -- Options for HTML output ------------------------------------------------- @@ -85,7 +174,7 @@ # # html_theme = 'alabaster' -html_logo = 'ash.png' +# Logo is configured in html_theme_options for Furo theme # The name of an image file (relative to this directory) to use as a favicon of # the docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32 @@ -95,4 +184,4 @@ # Add any paths that contain custom static files (such as style sheets) here, # relative to this directory. They are copied after the builtin static files, # so a file named "default.css" will overwrite the builtin "default.css". -html_static_path = ['_static'] +html_static_path = ["_static"] diff --git a/docs/index.rst b/docs/index.rst old mode 100644 new mode 100755 index 860a1ac..fe3bf1f --- a/docs/index.rst +++ b/docs/index.rst @@ -9,7 +9,7 @@ If you would like to test ``ash_model`` functionalities without installing it on ================ =================== ================== ========== =============== **Date** **Python Versions** **Main Author** **GitHub** **pypl** - 2023 3.9 `Giulio Rossetti`_ `Source`_ `Distribution`_ + 2025 3.9 `Giulio Rossetti`_ `Source`_ `Distribution`_ ================ =================== ================== ========== =============== @@ -19,8 +19,8 @@ Ash Dev Team ======================= ============================== **Name** **Contribution** -`Giulio Rossetti`_ Library Design, implementation -`Andrea Failla`_ Implementation, Documentation +`Giulio Rossetti`_ Library Design, Implementation +`Andrea Failla`_ Library Design, Implementation, Documentation `Salvatore Citraro`_ Implementation ======================= ============================== @@ -33,10 +33,9 @@ Ash Dev Team tutorial.rst install.rst - .. _`Giulio Rossetti`: http://www.about.giuliorossetti.net -.. _`Andrea Failla`: https://github.com/andreafailla +.. _`Andrea Failla`: https://andreafailla.github.io .. _`Salvatore Citraro`: https://github.com/dsalvaz .. _`Source`: https://github.com/GiulioRossetti/ASH -.. _`Distribution`: https://pypi.python.org/pypi/ASH +.. _`Distribution`: https://pypi.python.org/pypi/ash_model .. _`SoBigData++`: https://sobigdata.d4science.org/group/sobigdata-gateway/explore?siteId=20371853 \ No newline at end of file diff --git a/docs/install.rst b/docs/install.rst old mode 100644 new mode 100755 diff --git a/docs/overview.rst b/docs/overview.rst old mode 100644 new mode 100755 index 7516799..87a3b90 --- a/docs/overview.rst +++ b/docs/overview.rst @@ -14,7 +14,7 @@ The potential audience for ``Ash`` includes mathematicians, physicists, biologis Goals ----- -``Ash`` is built upon the halp_ python hypergraph library and is intended to provide: +``Ash`` is a python temporal hypergraph library providing: - tools for the study dynamic social, biological, and infrastructure hypernetworks, - a rapid development environment for collaborative, multidisciplinary, projects. diff --git a/docs/reference/_autosummary/classes/ash_model.ASH.rst b/docs/reference/_autosummary/classes/ash_model.ASH.rst new file mode 100644 index 0000000..56ea408 --- /dev/null +++ b/docs/reference/_autosummary/classes/ash_model.ASH.rst @@ -0,0 +1,75 @@ +ash\_model.ASH +============== + +.. currentmodule:: ash_model + +.. autoclass:: ASH + + + .. automethod:: __init__ + + + .. rubric:: Methods + + .. autosummary:: + + ~ASH.__init__ + ~ASH.add_hyperedge + ~ASH.add_hyperedges + ~ASH.add_node + ~ASH.add_nodes + ~ASH.avg_number_of_hyperedges + ~ASH.avg_number_of_nodes + ~ASH.bipartite_projection + ~ASH.clique_projection + ~ASH.coverage + ~ASH.degree + ~ASH.degree_by_hyperedge_size + ~ASH.degree_distribution + ~ASH.dual_hypergraph + ~ASH.get_hyperedge_attribute + ~ASH.get_hyperedge_attributes + ~ASH.get_hyperedge_id + ~ASH.get_hyperedge_nodes + ~ASH.get_hyperedge_weight + ~ASH.get_node_attribute + ~ASH.get_node_attributes + ~ASH.get_node_profile + ~ASH.get_node_profiles_by_time + ~ASH.get_s_incident + ~ASH.has_hyperedge + ~ASH.has_node + ~ASH.hyperedge_contribution + ~ASH.hyperedge_presence + ~ASH.hyperedge_size_distribution + ~ASH.hyperedges + ~ASH.induced_hypergraph + ~ASH.list_hyperedge_attributes + ~ASH.list_node_attributes + ~ASH.neighbors + ~ASH.node_contribution + ~ASH.node_presence + ~ASH.nodes + ~ASH.number_of_hyperedges + ~ASH.number_of_neighbors + ~ASH.number_of_nodes + ~ASH.remove_hyperedge + ~ASH.remove_hyperedges + ~ASH.remove_node + ~ASH.remove_nodes + ~ASH.remove_unlabelled_nodes + ~ASH.s_degree + ~ASH.s_line_graph + ~ASH.size + ~ASH.star + ~ASH.stream_interactions + ~ASH.temporal_slice + ~ASH.temporal_snapshots_ids + ~ASH.to_dict + ~ASH.uniformity + + + + + + \ No newline at end of file diff --git a/docs/reference/_autosummary/classes/ash_model.DensePresenceStore.rst b/docs/reference/_autosummary/classes/ash_model.DensePresenceStore.rst new file mode 100644 index 0000000..dcf65fb --- /dev/null +++ b/docs/reference/_autosummary/classes/ash_model.DensePresenceStore.rst @@ -0,0 +1,39 @@ +ash\_model.DensePresenceStore +============================= + +.. currentmodule:: ash_model + +.. autoclass:: DensePresenceStore + + + .. automethod:: __init__ + + + .. rubric:: Methods + + .. autosummary:: + + ~DensePresenceStore.__init__ + ~DensePresenceStore.clear + ~DensePresenceStore.copy + ~DensePresenceStore.fromkeys + ~DensePresenceStore.get + ~DensePresenceStore.items + ~DensePresenceStore.keys + ~DensePresenceStore.pop + ~DensePresenceStore.popitem + ~DensePresenceStore.setdefault + ~DensePresenceStore.update + ~DensePresenceStore.values + + + + + + .. rubric:: Attributes + + .. autosummary:: + + ~DensePresenceStore.default_factory + + \ No newline at end of file diff --git a/docs/reference/_autosummary/classes/ash_model.IntervalPresenceStore.rst b/docs/reference/_autosummary/classes/ash_model.IntervalPresenceStore.rst new file mode 100644 index 0000000..ebedf5a --- /dev/null +++ b/docs/reference/_autosummary/classes/ash_model.IntervalPresenceStore.rst @@ -0,0 +1,25 @@ +ash\_model.IntervalPresenceStore +================================ + +.. currentmodule:: ash_model + +.. autoclass:: IntervalPresenceStore + + + .. automethod:: __init__ + + + .. rubric:: Methods + + .. autosummary:: + + ~IntervalPresenceStore.__init__ + ~IntervalPresenceStore.get + ~IntervalPresenceStore.keys + ~IntervalPresenceStore.setdefault + + + + + + \ No newline at end of file diff --git a/docs/reference/_autosummary/classes/ash_model.NProfile.rst b/docs/reference/_autosummary/classes/ash_model.NProfile.rst new file mode 100644 index 0000000..7986bc8 --- /dev/null +++ b/docs/reference/_autosummary/classes/ash_model.NProfile.rst @@ -0,0 +1,33 @@ +ash\_model.NProfile +=================== + +.. currentmodule:: ash_model + +.. autoclass:: NProfile + + + .. automethod:: __init__ + + + .. rubric:: Methods + + .. autosummary:: + + ~NProfile.__init__ + ~NProfile.add_attribute + ~NProfile.add_attributes + ~NProfile.add_statistic + ~NProfile.attribute_computed_statistics + ~NProfile.get_attribute + ~NProfile.get_attributes + ~NProfile.get_statistic + ~NProfile.has_attribute + ~NProfile.has_statistic + ~NProfile.items + ~NProfile.to_dict + + + + + + \ No newline at end of file diff --git a/docs/reference/_autosummary/classes/ash_model.PresenceStore.rst b/docs/reference/_autosummary/classes/ash_model.PresenceStore.rst new file mode 100644 index 0000000..7c1a8d3 --- /dev/null +++ b/docs/reference/_autosummary/classes/ash_model.PresenceStore.rst @@ -0,0 +1,25 @@ +ash\_model.PresenceStore +======================== + +.. currentmodule:: ash_model + +.. autoclass:: PresenceStore + + + .. automethod:: __init__ + + + .. rubric:: Methods + + .. autosummary:: + + ~PresenceStore.__init__ + ~PresenceStore.get + ~PresenceStore.keys + ~PresenceStore.setdefault + + + + + + \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.attribute_consistency.rst b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.attribute_consistency.rst new file mode 100644 index 0000000..d976a30 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.attribute_consistency.rst @@ -0,0 +1,6 @@ +ash\_model.measures.attribute\_analysis.attribute\_consistency +============================================================== + +.. currentmodule:: ash_model.measures.attribute_analysis + +.. autofunction:: attribute_consistency \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.average_group_degree.rst b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.average_group_degree.rst new file mode 100644 index 0000000..2aceddb --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.average_group_degree.rst @@ -0,0 +1,6 @@ +ash\_model.measures.attribute\_analysis.average\_group\_degree +============================================================== + +.. currentmodule:: ash_model.measures.attribute_analysis + +.. autofunction:: average_group_degree \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.hyperedge_profile_entropy.rst b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.hyperedge_profile_entropy.rst new file mode 100644 index 0000000..4ef5e8e --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.hyperedge_profile_entropy.rst @@ -0,0 +1,6 @@ +ash\_model.measures.attribute\_analysis.hyperedge\_profile\_entropy +=================================================================== + +.. currentmodule:: ash_model.measures.attribute_analysis + +.. autofunction:: hyperedge_profile_entropy \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.hyperedge_profile_purity.rst b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.hyperedge_profile_purity.rst new file mode 100644 index 0000000..ab4c1f7 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.hyperedge_profile_purity.rst @@ -0,0 +1,6 @@ +ash\_model.measures.attribute\_analysis.hyperedge\_profile\_purity +================================================================== + +.. currentmodule:: ash_model.measures.attribute_analysis + +.. autofunction:: hyperedge_profile_purity \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.star_profile_entropy.rst b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.star_profile_entropy.rst new file mode 100644 index 0000000..29b52d0 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.star_profile_entropy.rst @@ -0,0 +1,6 @@ +ash\_model.measures.attribute\_analysis.star\_profile\_entropy +============================================================== + +.. currentmodule:: ash_model.measures.attribute_analysis + +.. autofunction:: star_profile_entropy \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.star_profile_homogeneity.rst b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.star_profile_homogeneity.rst new file mode 100644 index 0000000..c78e7c4 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.attribute_analysis.star_profile_homogeneity.rst @@ -0,0 +1,6 @@ +ash\_model.measures.attribute\_analysis.star\_profile\_homogeneity +================================================================== + +.. currentmodule:: ash_model.measures.attribute_analysis + +.. autofunction:: star_profile_homogeneity \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.clustering.average_s_local_clustering_coefficient.rst b/docs/reference/_autosummary/measures/ash_model.measures.clustering.average_s_local_clustering_coefficient.rst new file mode 100644 index 0000000..2f0987e --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.clustering.average_s_local_clustering_coefficient.rst @@ -0,0 +1,6 @@ +ash\_model.measures.clustering.average\_s\_local\_clustering\_coefficient +========================================================================= + +.. currentmodule:: ash_model.measures.clustering + +.. autofunction:: average_s_local_clustering_coefficient \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.clustering.inclusiveness.rst b/docs/reference/_autosummary/measures/ash_model.measures.clustering.inclusiveness.rst new file mode 100644 index 0000000..d963b0e --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.clustering.inclusiveness.rst @@ -0,0 +1,6 @@ +ash\_model.measures.clustering.inclusiveness +============================================ + +.. currentmodule:: ash_model.measures.clustering + +.. autofunction:: inclusiveness \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.clustering.s_intersections.rst b/docs/reference/_autosummary/measures/ash_model.measures.clustering.s_intersections.rst new file mode 100644 index 0000000..a23c0ad --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.clustering.s_intersections.rst @@ -0,0 +1,6 @@ +ash\_model.measures.clustering.s\_intersections +=============================================== + +.. currentmodule:: ash_model.measures.clustering + +.. autofunction:: s_intersections \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.clustering.s_local_clustering_coefficient.rst b/docs/reference/_autosummary/measures/ash_model.measures.clustering.s_local_clustering_coefficient.rst new file mode 100644 index 0000000..937b460 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.clustering.s_local_clustering_coefficient.rst @@ -0,0 +1,6 @@ +ash\_model.measures.clustering.s\_local\_clustering\_coefficient +================================================================ + +.. currentmodule:: ash_model.measures.clustering + +.. autofunction:: s_local_clustering_coefficient \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.hyper_conformity.hyper_conformity.rst b/docs/reference/_autosummary/measures/ash_model.measures.hyper_conformity.hyper_conformity.rst new file mode 100644 index 0000000..097ce49 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.hyper_conformity.hyper_conformity.rst @@ -0,0 +1,6 @@ +ash\_model.measures.hyper\_conformity.hyper\_conformity +======================================================= + +.. currentmodule:: ash_model.measures.hyper_conformity + +.. autofunction:: hyper_conformity \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_betweenness_centrality.rst b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_betweenness_centrality.rst new file mode 100644 index 0000000..2ecf693 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_betweenness_centrality.rst @@ -0,0 +1,6 @@ +ash\_model.measures.s\_centralities.s\_betweenness\_centrality +============================================================== + +.. currentmodule:: ash_model.measures.s_centralities + +.. autofunction:: s_betweenness_centrality \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_closeness_centrality.rst b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_closeness_centrality.rst new file mode 100644 index 0000000..a752157 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_closeness_centrality.rst @@ -0,0 +1,6 @@ +ash\_model.measures.s\_centralities.s\_closeness\_centrality +============================================================ + +.. currentmodule:: ash_model.measures.s_centralities + +.. autofunction:: s_closeness_centrality \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_eccentricity.rst b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_eccentricity.rst new file mode 100644 index 0000000..8e96373 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_eccentricity.rst @@ -0,0 +1,6 @@ +ash\_model.measures.s\_centralities.s\_eccentricity +=================================================== + +.. currentmodule:: ash_model.measures.s_centralities + +.. autofunction:: s_eccentricity \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_eigenvector_centrality.rst b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_eigenvector_centrality.rst new file mode 100644 index 0000000..e307329 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_eigenvector_centrality.rst @@ -0,0 +1,6 @@ +ash\_model.measures.s\_centralities.s\_eigenvector\_centrality +============================================================== + +.. currentmodule:: ash_model.measures.s_centralities + +.. autofunction:: s_eigenvector_centrality \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_harmonic_centrality.rst b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_harmonic_centrality.rst new file mode 100644 index 0000000..33048ab --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_harmonic_centrality.rst @@ -0,0 +1,6 @@ +ash\_model.measures.s\_centralities.s\_harmonic\_centrality +=========================================================== + +.. currentmodule:: ash_model.measures.s_centralities + +.. autofunction:: s_harmonic_centrality \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_katz.rst b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_katz.rst new file mode 100644 index 0000000..08c1e35 --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_katz.rst @@ -0,0 +1,6 @@ +ash\_model.measures.s\_centralities.s\_katz +=========================================== + +.. currentmodule:: ash_model.measures.s_centralities + +.. autofunction:: s_katz \ No newline at end of file diff --git a/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_load_centrality.rst b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_load_centrality.rst new file mode 100644 index 0000000..929427d --- /dev/null +++ b/docs/reference/_autosummary/measures/ash_model.measures.s_centralities.s_load_centrality.rst @@ -0,0 +1,6 @@ +ash\_model.measures.s\_centralities.s\_load\_centrality +======================================================= + +.. currentmodule:: ash_model.measures.s_centralities + +.. autofunction:: s_load_centrality \ No newline at end of file diff --git a/docs/reference/_autosummary/multiego/ash_model.multiego.delta_similarity.rst b/docs/reference/_autosummary/multiego/ash_model.multiego.delta_similarity.rst new file mode 100644 index 0000000..cfb2ad1 --- /dev/null +++ b/docs/reference/_autosummary/multiego/ash_model.multiego.delta_similarity.rst @@ -0,0 +1,6 @@ +ash\_model.multiego.delta\_similarity +===================================== + +.. currentmodule:: ash_model.multiego + +.. autofunction:: delta_similarity \ No newline at end of file diff --git a/docs/reference/_autosummary/multiego/ash_model.multiego.get_core_multiego.rst b/docs/reference/_autosummary/multiego/ash_model.multiego.get_core_multiego.rst new file mode 100644 index 0000000..2ffbcba --- /dev/null +++ b/docs/reference/_autosummary/multiego/ash_model.multiego.get_core_multiego.rst @@ -0,0 +1,6 @@ +ash\_model.multiego.get\_core\_multiego +======================================= + +.. currentmodule:: ash_model.multiego + +.. autofunction:: get_core_multiego \ No newline at end of file diff --git a/docs/reference/_autosummary/multiego/ash_model.multiego.get_fractured_multiego.rst b/docs/reference/_autosummary/multiego/ash_model.multiego.get_fractured_multiego.rst new file mode 100644 index 0000000..ba414f7 --- /dev/null +++ b/docs/reference/_autosummary/multiego/ash_model.multiego.get_fractured_multiego.rst @@ -0,0 +1,6 @@ +ash\_model.multiego.get\_fractured\_multiego +============================================ + +.. currentmodule:: ash_model.multiego + +.. autofunction:: get_fractured_multiego \ No newline at end of file diff --git a/docs/reference/_autosummary/multiego/ash_model.multiego.get_multiego.rst b/docs/reference/_autosummary/multiego/ash_model.multiego.get_multiego.rst new file mode 100644 index 0000000..435adc6 --- /dev/null +++ b/docs/reference/_autosummary/multiego/ash_model.multiego.get_multiego.rst @@ -0,0 +1,6 @@ +ash\_model.multiego.get\_multiego +================================= + +.. currentmodule:: ash_model.multiego + +.. autofunction:: get_multiego \ No newline at end of file diff --git a/docs/reference/_autosummary/multiego/ash_model.multiego.jaccard_similarity.rst b/docs/reference/_autosummary/multiego/ash_model.multiego.jaccard_similarity.rst new file mode 100644 index 0000000..9b2825c --- /dev/null +++ b/docs/reference/_autosummary/multiego/ash_model.multiego.jaccard_similarity.rst @@ -0,0 +1,6 @@ +ash\_model.multiego.jaccard\_similarity +======================================= + +.. currentmodule:: ash_model.multiego + +.. autofunction:: jaccard_similarity \ No newline at end of file diff --git a/docs/reference/_autosummary/multiego/ash_model.multiego.minimum_overlapping_similarity.rst b/docs/reference/_autosummary/multiego/ash_model.multiego.minimum_overlapping_similarity.rst new file mode 100644 index 0000000..4fd174d --- /dev/null +++ b/docs/reference/_autosummary/multiego/ash_model.multiego.minimum_overlapping_similarity.rst @@ -0,0 +1,6 @@ +ash\_model.multiego.minimum\_overlapping\_similarity +==================================================== + +.. currentmodule:: ash_model.multiego + +.. autofunction:: minimum_overlapping_similarity \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.randwalks.random_walk_probabilities.rst b/docs/reference/_autosummary/paths/ash_model.paths.randwalks.random_walk_probabilities.rst new file mode 100644 index 0000000..3d51405 --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.randwalks.random_walk_probabilities.rst @@ -0,0 +1,6 @@ +ash\_model.paths.randwalks.random\_walk\_probabilities +====================================================== + +.. currentmodule:: ash_model.paths.randwalks + +.. autofunction:: random_walk_probabilities \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.randwalks.random_walks.rst b/docs/reference/_autosummary/paths/ash_model.paths.randwalks.random_walks.rst new file mode 100644 index 0000000..eb3f3b2 --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.randwalks.random_walks.rst @@ -0,0 +1,6 @@ +ash\_model.paths.randwalks.random\_walks +======================================== + +.. currentmodule:: ash_model.paths.randwalks + +.. autofunction:: random_walks \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.randwalks.time_respecting_random_walks.rst b/docs/reference/_autosummary/paths/ash_model.paths.randwalks.time_respecting_random_walks.rst new file mode 100644 index 0000000..cf0d38b --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.randwalks.time_respecting_random_walks.rst @@ -0,0 +1,6 @@ +ash\_model.paths.randwalks.time\_respecting\_random\_walks +========================================================== + +.. currentmodule:: ash_model.paths.randwalks + +.. autofunction:: time_respecting_random_walks \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.all_time_respecting_s_walks.rst b/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.all_time_respecting_s_walks.rst new file mode 100644 index 0000000..14167b4 --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.all_time_respecting_s_walks.rst @@ -0,0 +1,6 @@ +ash\_model.paths.time\_respecting\_walks.all\_time\_respecting\_s\_walks +======================================================================== + +.. currentmodule:: ash_model.paths.time_respecting_walks + +.. autofunction:: all_time_respecting_s_walks \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.temporal_s_dag.rst b/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.temporal_s_dag.rst new file mode 100644 index 0000000..9d01e9b --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.temporal_s_dag.rst @@ -0,0 +1,6 @@ +ash\_model.paths.time\_respecting\_walks.temporal\_s\_dag +========================================================= + +.. currentmodule:: ash_model.paths.time_respecting_walks + +.. autofunction:: temporal_s_dag \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.time_respecting_s_walks.rst b/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.time_respecting_s_walks.rst new file mode 100644 index 0000000..915e06c --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.time_respecting_walks.time_respecting_s_walks.rst @@ -0,0 +1,6 @@ +ash\_model.paths.time\_respecting\_walks.time\_respecting\_s\_walks +=================================================================== + +.. currentmodule:: ash_model.paths.time_respecting_walks + +.. autofunction:: time_respecting_s_walks \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_path_lengths.rst b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_path_lengths.rst new file mode 100644 index 0000000..a8010b7 --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_path_lengths.rst @@ -0,0 +1,6 @@ +ash\_model.paths.walks.all\_shortest\_s\_path\_lengths +====================================================== + +.. currentmodule:: ash_model.paths.walks + +.. autofunction:: all_shortest_s_path_lengths \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_paths.rst b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_paths.rst new file mode 100644 index 0000000..fb1c2df --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_paths.rst @@ -0,0 +1,6 @@ +ash\_model.paths.walks.all\_shortest\_s\_paths +============================================== + +.. currentmodule:: ash_model.paths.walks + +.. autofunction:: all_shortest_s_paths \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_walk_lengths.rst b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_walk_lengths.rst new file mode 100644 index 0000000..7211698 --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_walk_lengths.rst @@ -0,0 +1,6 @@ +ash\_model.paths.walks.all\_shortest\_s\_walk\_lengths +====================================================== + +.. currentmodule:: ash_model.paths.walks + +.. autofunction:: all_shortest_s_walk_lengths \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_walks.rst b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_walks.rst new file mode 100644 index 0000000..b02dbef --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_shortest_s_walks.rst @@ -0,0 +1,6 @@ +ash\_model.paths.walks.all\_shortest\_s\_walks +============================================== + +.. currentmodule:: ash_model.paths.walks + +.. autofunction:: all_shortest_s_walks \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.walks.all_simple_paths.rst b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_simple_paths.rst new file mode 100644 index 0000000..f9c8e90 --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.walks.all_simple_paths.rst @@ -0,0 +1,6 @@ +ash\_model.paths.walks.all\_simple\_paths +========================================= + +.. currentmodule:: ash_model.paths.walks + +.. autofunction:: all_simple_paths \ No newline at end of file diff --git a/docs/reference/_autosummary/paths/ash_model.paths.walks.shortest_s_path.rst b/docs/reference/_autosummary/paths/ash_model.paths.walks.shortest_s_path.rst new file mode 100644 index 0000000..ab1375c --- /dev/null +++ b/docs/reference/_autosummary/paths/ash_model.paths.walks.shortest_s_path.rst @@ -0,0 +1,6 @@ +ash\_model.paths.walks.shortest\_s\_path +======================================== + +.. currentmodule:: ash_model.paths.walks + +.. autofunction:: shortest_s_path \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_ash_from_json.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_ash_from_json.rst new file mode 100644 index 0000000..73b9f57 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_ash_from_json.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.read\_ash\_from\_json +============================================= + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: read_ash_from_json \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_hif.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_hif.rst new file mode 100644 index 0000000..196fc81 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_hif.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.read\_hif +================================= + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: read_hif \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_profiles_from_csv.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_profiles_from_csv.rst new file mode 100644 index 0000000..0963e60 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_profiles_from_csv.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.read\_profiles\_from\_csv +================================================= + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: read_profiles_from_csv \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_profiles_from_jsonl.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_profiles_from_jsonl.rst new file mode 100644 index 0000000..8a42327 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_profiles_from_jsonl.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.read\_profiles\_from\_jsonl +=================================================== + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: read_profiles_from_jsonl \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_sh_from_csv.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_sh_from_csv.rst new file mode 100644 index 0000000..f929de2 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.read_sh_from_csv.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.read\_sh\_from\_csv +=========================================== + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: read_sh_from_csv \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_ash_to_json.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_ash_to_json.rst new file mode 100644 index 0000000..62e7797 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_ash_to_json.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.write\_ash\_to\_json +============================================ + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: write_ash_to_json \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_hif.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_hif.rst new file mode 100644 index 0000000..9b42662 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_hif.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.write\_hif +================================== + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: write_hif \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_profiles_to_csv.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_profiles_to_csv.rst new file mode 100644 index 0000000..5dadbb1 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_profiles_to_csv.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.write\_profiles\_to\_csv +================================================ + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: write_profiles_to_csv \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_profiles_to_jsonl.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_profiles_to_jsonl.rst new file mode 100644 index 0000000..37ad5d5 --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_profiles_to_jsonl.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.write\_profiles\_to\_jsonl +================================================== + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: write_profiles_to_jsonl \ No newline at end of file diff --git a/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_sh_to_csv.rst b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_sh_to_csv.rst new file mode 100644 index 0000000..90a06ee --- /dev/null +++ b/docs/reference/_autosummary/readwrite/ash_model.readwrite.io.write_sh_to_csv.rst @@ -0,0 +1,6 @@ +ash\_model.readwrite.io.write\_sh\_to\_csv +========================================== + +.. currentmodule:: ash_model.readwrite.io + +.. autofunction:: write_sh_to_csv \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.matrices.adjacency_matrix.rst b/docs/reference/_autosummary/utils/ash_model.utils.matrices.adjacency_matrix.rst new file mode 100644 index 0000000..304f35c --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.matrices.adjacency_matrix.rst @@ -0,0 +1,6 @@ +ash\_model.utils.matrices.adjacency\_matrix +=========================================== + +.. currentmodule:: ash_model.utils.matrices + +.. autofunction:: adjacency_matrix \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.matrices.adjacency_matrix_by_time.rst b/docs/reference/_autosummary/utils/ash_model.utils.matrices.adjacency_matrix_by_time.rst new file mode 100644 index 0000000..6155d03 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.matrices.adjacency_matrix_by_time.rst @@ -0,0 +1,6 @@ +ash\_model.utils.matrices.adjacency\_matrix\_by\_time +===================================================== + +.. currentmodule:: ash_model.utils.matrices + +.. autofunction:: adjacency_matrix_by_time \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.matrices.get_hyperedge_id_mapping.rst b/docs/reference/_autosummary/utils/ash_model.utils.matrices.get_hyperedge_id_mapping.rst new file mode 100644 index 0000000..79cbc24 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.matrices.get_hyperedge_id_mapping.rst @@ -0,0 +1,6 @@ +ash\_model.utils.matrices.get\_hyperedge\_id\_mapping +===================================================== + +.. currentmodule:: ash_model.utils.matrices + +.. autofunction:: get_hyperedge_id_mapping \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.matrices.get_node_id_mapping.rst b/docs/reference/_autosummary/utils/ash_model.utils.matrices.get_node_id_mapping.rst new file mode 100644 index 0000000..9b29317 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.matrices.get_node_id_mapping.rst @@ -0,0 +1,6 @@ +ash\_model.utils.matrices.get\_node\_id\_mapping +================================================ + +.. currentmodule:: ash_model.utils.matrices + +.. autofunction:: get_node_id_mapping \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.matrices.incidence_matrix.rst b/docs/reference/_autosummary/utils/ash_model.utils.matrices.incidence_matrix.rst new file mode 100644 index 0000000..44f376a --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.matrices.incidence_matrix.rst @@ -0,0 +1,6 @@ +ash\_model.utils.matrices.incidence\_matrix +=========================================== + +.. currentmodule:: ash_model.utils.matrices + +.. autofunction:: incidence_matrix \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.matrices.incidence_matrix_by_time.rst b/docs/reference/_autosummary/utils/ash_model.utils.matrices.incidence_matrix_by_time.rst new file mode 100644 index 0000000..bed35c5 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.matrices.incidence_matrix_by_time.rst @@ -0,0 +1,6 @@ +ash\_model.utils.matrices.incidence\_matrix\_by\_time +===================================================== + +.. currentmodule:: ash_model.utils.matrices + +.. autofunction:: incidence_matrix_by_time \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_bipartite.rst b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_bipartite.rst new file mode 100644 index 0000000..52eb982 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_bipartite.rst @@ -0,0 +1,6 @@ +ash\_model.utils.networkx.from\_networkx\_bipartite +=================================================== + +.. currentmodule:: ash_model.utils.networkx + +.. autofunction:: from_networkx_bipartite \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_bipartite_list.rst b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_bipartite_list.rst new file mode 100644 index 0000000..d43a62a --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_bipartite_list.rst @@ -0,0 +1,6 @@ +ash\_model.utils.networkx.from\_networkx\_bipartite\_list +========================================================= + +.. currentmodule:: ash_model.utils.networkx + +.. autofunction:: from_networkx_bipartite_list \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_graph.rst b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_graph.rst new file mode 100644 index 0000000..7b8880f --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_graph.rst @@ -0,0 +1,6 @@ +ash\_model.utils.networkx.from\_networkx\_graph +=============================================== + +.. currentmodule:: ash_model.utils.networkx + +.. autofunction:: from_networkx_graph \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_graph_list.rst b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_graph_list.rst new file mode 100644 index 0000000..be5eac1 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_graph_list.rst @@ -0,0 +1,6 @@ +ash\_model.utils.networkx.from\_networkx\_graph\_list +===================================================== + +.. currentmodule:: ash_model.utils.networkx + +.. autofunction:: from_networkx_graph_list \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_maximal_cliques.rst b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_maximal_cliques.rst new file mode 100644 index 0000000..3537683 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_maximal_cliques.rst @@ -0,0 +1,6 @@ +ash\_model.utils.networkx.from\_networkx\_maximal\_cliques +========================================================== + +.. currentmodule:: ash_model.utils.networkx + +.. autofunction:: from_networkx_maximal_cliques \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_maximal_cliques_list.rst b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_maximal_cliques_list.rst new file mode 100644 index 0000000..4fdf57d --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.networkx.from_networkx_maximal_cliques_list.rst @@ -0,0 +1,6 @@ +ash\_model.utils.networkx.from\_networkx\_maximal\_cliques\_list +================================================================ + +.. currentmodule:: ash_model.utils.networkx + +.. autofunction:: from_networkx_maximal_cliques_list \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.profiles.aggregate_node_profile.rst b/docs/reference/_autosummary/utils/ash_model.utils.profiles.aggregate_node_profile.rst new file mode 100644 index 0000000..d78218c --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.profiles.aggregate_node_profile.rst @@ -0,0 +1,6 @@ +ash\_model.utils.profiles.aggregate\_node\_profile +================================================== + +.. currentmodule:: ash_model.utils.profiles + +.. autofunction:: aggregate_node_profile \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.profiles.hyperedge_aggregate_node_profile.rst b/docs/reference/_autosummary/utils/ash_model.utils.profiles.hyperedge_aggregate_node_profile.rst new file mode 100644 index 0000000..4062890 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.profiles.hyperedge_aggregate_node_profile.rst @@ -0,0 +1,6 @@ +ash\_model.utils.profiles.hyperedge\_aggregate\_node\_profile +============================================================= + +.. currentmodule:: ash_model.utils.profiles + +.. autofunction:: hyperedge_aggregate_node_profile \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.profiles.hyperedge_most_frequent_node_attribute_value.rst b/docs/reference/_autosummary/utils/ash_model.utils.profiles.hyperedge_most_frequent_node_attribute_value.rst new file mode 100644 index 0000000..c7a25fb --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.profiles.hyperedge_most_frequent_node_attribute_value.rst @@ -0,0 +1,6 @@ +ash\_model.utils.profiles.hyperedge\_most\_frequent\_node\_attribute\_value +=========================================================================== + +.. currentmodule:: ash_model.utils.profiles + +.. autofunction:: hyperedge_most_frequent_node_attribute_value \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.bipartite_projection.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.bipartite_projection.rst new file mode 100644 index 0000000..dbd0079 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.bipartite_projection.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.bipartite\_projection +================================================== + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: bipartite_projection \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.bipartite_projection_by_time.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.bipartite_projection_by_time.rst new file mode 100644 index 0000000..6ed13ec --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.bipartite_projection_by_time.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.bipartite\_projection\_by\_time +============================================================ + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: bipartite_projection_by_time \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.clique_projection.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.clique_projection.rst new file mode 100644 index 0000000..ee44968 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.clique_projection.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.clique\_projection +=============================================== + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: clique_projection \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.clique_projection_by_time.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.clique_projection_by_time.rst new file mode 100644 index 0000000..3b8775d --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.clique_projection_by_time.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.clique\_projection\_by\_time +========================================================= + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: clique_projection_by_time \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.dual_hypergraph_projection.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.dual_hypergraph_projection.rst new file mode 100644 index 0000000..e67b5e0 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.dual_hypergraph_projection.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.dual\_hypergraph\_projection +========================================================= + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: dual_hypergraph_projection \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.dual_hypergraph_projection_by_time.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.dual_hypergraph_projection_by_time.rst new file mode 100644 index 0000000..d771e0e --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.dual_hypergraph_projection_by_time.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.dual\_hypergraph\_projection\_by\_time +=================================================================== + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: dual_hypergraph_projection_by_time \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.line_graph_projection.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.line_graph_projection.rst new file mode 100644 index 0000000..5d847d5 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.line_graph_projection.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.line\_graph\_projection +==================================================== + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: line_graph_projection \ No newline at end of file diff --git a/docs/reference/_autosummary/utils/ash_model.utils.projections.line_graph_projection_by_time.rst b/docs/reference/_autosummary/utils/ash_model.utils.projections.line_graph_projection_by_time.rst new file mode 100644 index 0000000..91a2293 --- /dev/null +++ b/docs/reference/_autosummary/utils/ash_model.utils.projections.line_graph_projection_by_time.rst @@ -0,0 +1,6 @@ +ash\_model.utils.projections.line\_graph\_projection\_by\_time +============================================================== + +.. currentmodule:: ash_model.utils.projections + +.. autofunction:: line_graph_projection_by_time \ No newline at end of file diff --git a/docs/reference/classes.rst b/docs/reference/classes.rst old mode 100644 new mode 100755 index cc92ed8..6d10fdf --- a/docs/reference/classes.rst +++ b/docs/reference/classes.rst @@ -1,15 +1,98 @@ -******* Classes -******* +======= + +Overview of the core package classes. + +Summary +------- .. currentmodule:: ash_model -.. autoclass:: ASH + +.. autosummary:: + :toctree: _autosummary/classes + :nosignatures: + + ASH + NProfile + PresenceStore + DensePresenceStore + IntervalPresenceStore + +Details +------- + +.. note:: + + The ASH class acts as the core data structure for representing temporal hypergraphs. It encapsulates nodes, hyperedges, attributes and their temporal dynamics, providing methods for manipulation and analysis. + + +.. automodule:: ash_model.classes.undirected :members: :undoc-members: + :inherited-members: :show-inheritance: + :no-index: -.. currentmodule:: ash_model -.. autoclass:: NProfile + +.. note:: + + The NProfile class is designed to manage all attributes related to a node within the ASH framework. It supports various data types and provides functionality for adding, updating, and querying node attributes over time. + +.. automodule:: ash_model.classes.node_profile + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: + + +.. note:: + The PresenceStore class and its subclasses (DensePresenceStore, IntervalPresenceStore) are specialized data structures for efficiently storing and querying the temporal presence of hyperedges within the ASH model. They support different storage strategies to optimize for various use cases and performance requirements. + +Backend Selection +~~~~~~~~~~~~~~~~~ + +ASH supports two backend implementations for managing temporal presence: + +**Dense Backend** (default) + - **Storage**: Direct mapping ``time → set(hyperedge_ids)`` + - **Best for**: Dense timelines, frequent snapshot queries, shorter time spans + - **Complexity**: O(1) snapshot access, O(1) per-time updates + - **Memory**: Proportional to number of distinct time points + +**Interval Backend** + - **Storage**: Sparse representation ``hyperedge_id → list[(start, end)]`` with optimized event-diff indexing + - **Best for**: Long sparse intervals, bulk interval operations, memory-constrained environments + - **Complexity**: O(log k) snapshot materialization via bisect (k = intervals per id), O(1) interval add/remove + - **Memory**: Proportional to number of intervals (typically much smaller for sparse data) + +Usage example:: + + # Default dense backend + H = ASH() + + # Interval backend for sparse temporal data + H_sparse = ASH(backend="interval") + + # Both backends provide identical API + H.add_hyperedge([1, 2, 3], start=0, end=100) + H_sparse.add_hyperedge([1, 2, 3], start=0, end=100) + +Technical Note +~~~~~~~~~~~~~~ + +The **IntervalPresenceStore** implements two key optimizations: + +1. **Binary search for presence queries**: Maintains a parallel ``starts`` list for each hyperedge's intervals, enabling O(log k) lookup instead of O(k) linear scan. + +2. **Event-diff for interval updates**: Uses a difference array (``_time_events``) to represent interval boundaries. Adding/removing an interval requires only O(1) event updates instead of O(length) per-time operations. The full time→count mapping is rebuilt lazily when ``keys()`` is called. + +These optimizations make the interval backend practical for large-scale temporal networks with long, sparse activity patterns. + +.. automodule:: ash_model.classes.presence_store :members: :undoc-members: - :show-inheritance: \ No newline at end of file + :inherited-members: + :show-inheritance: + :no-index: + diff --git a/docs/reference/generators.rst b/docs/reference/generators.rst new file mode 100644 index 0000000..93bb56e --- /dev/null +++ b/docs/reference/generators.rst @@ -0,0 +1,14 @@ +Generators +========== + +.. automodule:: ash_model.generators.random + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + +.. automodule:: ash_model.generators.homophily_driven + :members: + :undoc-members: + :inherited-members: + :show-inheritance: diff --git a/docs/reference/measures_attribute_analysis.rst b/docs/reference/measures_attribute_analysis.rst new file mode 100755 index 0000000..09b4cb7 --- /dev/null +++ b/docs/reference/measures_attribute_analysis.rst @@ -0,0 +1,27 @@ +Attribute Analysis +================== + +Summary +------- + +.. currentmodule:: ash_model.measures.attribute_analysis +.. autosummary:: + :toctree: _autosummary/measures + :nosignatures: + + hyperedge_profile_purity + hyperedge_profile_entropy + star_profile_entropy + star_profile_homogeneity + average_group_degree + attribute_consistency + +Details +------- + +.. automodule:: ash_model.measures.attribute_analysis + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: \ No newline at end of file diff --git a/docs/reference/measures_clustering.rst b/docs/reference/measures_clustering.rst new file mode 100755 index 0000000..35486ff --- /dev/null +++ b/docs/reference/measures_clustering.rst @@ -0,0 +1,25 @@ +Clustering +========== + +Summary +------- + +.. currentmodule:: ash_model.measures.clustering +.. autosummary:: + :toctree: _autosummary/measures + :nosignatures: + + s_local_clustering_coefficient + average_s_local_clustering_coefficient + s_intersections + inclusiveness + +Details +------- + +.. automodule:: ash_model.measures.clustering + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/measures_hyper_conformity.rst b/docs/reference/measures_hyper_conformity.rst new file mode 100755 index 0000000..68d09d2 --- /dev/null +++ b/docs/reference/measures_hyper_conformity.rst @@ -0,0 +1,22 @@ +Hyper Conformity +================ + +Summary +------- + +.. currentmodule:: ash_model.measures.hyper_conformity +.. autosummary:: + :toctree: _autosummary/measures + :nosignatures: + + hyper_conformity + +Details +------- + +.. automodule:: ash_model.measures.hyper_conformity + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/measures_hyper_segregation.rst b/docs/reference/measures_hyper_segregation.rst new file mode 100644 index 0000000..3a75f60 --- /dev/null +++ b/docs/reference/measures_hyper_segregation.rst @@ -0,0 +1,15 @@ +Hyper Segregation +================== + +Summary +------- + +Details +------- + +.. automodule:: ash_model.measures.hyper_segregation + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/measures_s_centralities.rst b/docs/reference/measures_s_centralities.rst new file mode 100755 index 0000000..8336cab --- /dev/null +++ b/docs/reference/measures_s_centralities.rst @@ -0,0 +1,28 @@ +Centralities +============ + +Summary +------- + +.. currentmodule:: ash_model.measures.s_centralities +.. autosummary:: + :toctree: _autosummary/measures + :nosignatures: + + s_betweenness_centrality + s_closeness_centrality + s_eccentricity + s_harmonic_centrality + s_katz + s_load_centrality + s_eigenvector_centrality + +Details +------- + +.. automodule:: ash_model.measures.s_centralities + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/multiego.rst b/docs/reference/multiego.rst new file mode 100644 index 0000000..0dad0ed --- /dev/null +++ b/docs/reference/multiego.rst @@ -0,0 +1,27 @@ +Multi-Ego Networks +================== + +Summary +------- + +.. currentmodule:: ash_model.multiego +.. autosummary:: + :toctree: _autosummary/multiego + :nosignatures: + + get_multiego + get_fractured_multiego + get_core_multiego + jaccard_similarity + minimum_overlapping_similarity + delta_similarity + +Details +------- + +.. automodule:: ash_model.multiego + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/paths_randwalks.rst b/docs/reference/paths_randwalks.rst new file mode 100755 index 0000000..667d054 --- /dev/null +++ b/docs/reference/paths_randwalks.rst @@ -0,0 +1,24 @@ +Random Walks +============ + +Summary +------- + +.. currentmodule:: ash_model.paths.randwalks +.. autosummary:: + :toctree: _autosummary/paths + :nosignatures: + + random_walk_probabilities + random_walks + time_respecting_random_walks + +Details +------- + +.. automodule:: ash_model.paths.randwalks + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/paths_time_respecting_walks.rst b/docs/reference/paths_time_respecting_walks.rst new file mode 100755 index 0000000..c6351aa --- /dev/null +++ b/docs/reference/paths_time_respecting_walks.rst @@ -0,0 +1,24 @@ +Time-Respecting Walks +===================== + +Summary +------- + +.. currentmodule:: ash_model.paths.time_respecting_walks +.. autosummary:: + :toctree: _autosummary/paths + :nosignatures: + + temporal_s_dag + time_respecting_s_walks + all_time_respecting_s_walks + +Details +------- + +.. automodule:: ash_model.paths.time_respecting_walks + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/paths_walks.rst b/docs/reference/paths_walks.rst new file mode 100755 index 0000000..1c2c9a9 --- /dev/null +++ b/docs/reference/paths_walks.rst @@ -0,0 +1,27 @@ +Walks +===== + +Summary +------- + +.. currentmodule:: ash_model.paths.walks +.. autosummary:: + :toctree: _autosummary/paths + :nosignatures: + + all_simple_paths + shortest_s_path + all_shortest_s_paths + all_shortest_s_path_lengths + all_shortest_s_walks + all_shortest_s_walk_lengths + +Details +------- + +.. automodule:: ash_model.paths.walks + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/readwrite.rst b/docs/reference/readwrite.rst old mode 100644 new mode 100755 index 4cc450f..4c43747 --- a/docs/reference/readwrite.rst +++ b/docs/reference/readwrite.rst @@ -1,30 +1,56 @@ -=== -I/O -=== +Read/Write +========== -.. automodule:: ash_model.readwrite - :members: +Summary +------- +The readwrite module provides functions for reading and writing ASH model data in various formats, including CSV, JSON/JSONL, and HIF (Hypergraph Interchange Format). These functions facilitate the import and export of profiles, social hypergraphs, and ASH models, enabling easy data manipulation and sharing. ---- +.. currentmodule:: ash_model.readwrite.io + CSV ---- +~~~ .. autosummary:: - :toctree: io/ + :toctree: _autosummary/readwrite + :nosignatures: - write_profiles_to_csv - read_profiles_from_csv - write_sh_to_csv - read_sh_from_csv + write_profiles_to_csv + read_profiles_from_csv + write_sh_to_csv + read_sh_from_csv ----- -JSON ----- +JSON / JSONL +~~~~~~~~~~~~ .. autosummary:: - :toctree: io/ + :toctree: _autosummary/readwrite + :nosignatures: - write_profiles_to_jsonl - read_profiles_from_jsonl - write_ash_to_json - read_ash_from_json \ No newline at end of file + write_profiles_to_jsonl + read_profiles_from_jsonl + write_ash_to_json + read_ash_from_json + +HIF +~~~ +HIF (Hypergraph Interchange Format) is a file format designed for representing hypergraphs. It is particularly useful for storing and exchanging hypergraph data due to its simplicity and human-readability. + +Read more about HIF `here `_ + + +.. autosummary:: + :toctree: _autosummary/readwrite + :nosignatures: + + write_hif + read_hif + +Details +------- + +.. automodule:: ash_model.readwrite.io + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/reference.rst b/docs/reference/reference.rst old mode 100644 new mode 100755 index b9a8096..ed50b3c --- a/docs/reference/reference.rst +++ b/docs/reference/reference.rst @@ -1,16 +1,98 @@ -********* Reference -********* +========= -``ash_model`` composes of several modules, each one fulfilling a different goal (modeling, analysis, visualization, I/O). +Below is a comprehensive overview of the ``ash_model`` API organized by module. +Classes +~~~~~~~~ + + +This module contains the core classes used in the ASH model. Specifically, it includes the ASH class to represent the model itself, and the NProfile class for node profiles. + +.. toctree:: + :maxdepth: 1 + + classes + + + + +Measures +~~~~~~~~~~~ + +This section includes various measures that can be computed on ASH models. + .. toctree:: - :maxdepth: 2 + :maxdepth: 1 + + measures_attribute_analysis + measures_clustering + measures_hyper_conformity + measures_hyper_segregation + measures_s_centralities + + +MultiEgo +~~~~~~~~ + +This module provides functions for multi-ego network analysis, including core identification, similarity measures, and fracture analysis. + +.. toctree:: + :maxdepth: 1 + + multiego + + +Generators +~~~~~~~~~~~ + +This module provides functions to generate synthetic ASH models with specific properties, such as random hypergraphs or hypergraphs with controlled attribute homogeneity. + +.. toctree:: + :maxdepth: 1 + + generators + + +Paths and Walks +~~~~~~~~~~~~~~~~ + +This module includes pathfinding and random walk generation algorithms for ASH models. +Notably, it includes s-walks and time-respecting walks. + +.. toctree:: + :maxdepth: 1 + + paths_walks + paths_time_respecting_walks + paths_randwalks + + +I/O +~~~ + +This module provides functions to import/export ASH models from/to JSON, CSV, and HIF. + +.. toctree:: + :maxdepth: 1 + + readwrite + +Utils +~~~~~ + +This module provides various utility functions for working with ASH models, including matrix transformations, projections, networkx conversions, and profile manipulations. + +.. toctree:: + :maxdepth: 1 + + utils + +Visualization +~~~~~~~~~~~~~ +.. toctree:: + :maxdepth: 1 + + viz - classes.rst - models.rst - paths.rst - readwrite.rst - viz.rst - utils.rst \ No newline at end of file diff --git a/docs/reference/utils.rst b/docs/reference/utils.rst old mode 100644 new mode 100755 index 56b0f76..b8d5f1d --- a/docs/reference/utils.rst +++ b/docs/reference/utils.rst @@ -1,37 +1,95 @@ -===== Utils ===== ----------------------------- -Undirected Graphs Transforms ----------------------------- +Summary +------- +The utils module provides various utility functions for working with ASH models, including matrix transformations, projections, and profile manipulations. + +Matrices +~~~~~~~~~~~~ +.. currentmodule:: ash_model.utils.matrices +.. autosummary:: + :toctree: _autosummary/utils + :nosignatures: -.. automodule:: ash_model.utils - :members: + get_hyperedge_id_mapping + get_node_id_mapping + incidence_matrix + incidence_matrix_by_time + adjacency_matrix + adjacency_matrix_by_time +Projections +~~~~~~~~~~~~ +.. currentmodule:: ash_model.utils.projections .. autosummary:: - :toctree: utils/ + :toctree: _autosummary/utils + :nosignatures: - to_graph_decomposition - to_networkx_graph - from_networkx_graph + clique_projection + bipartite_projection + line_graph_projection + dual_hypergraph_projection + clique_projection_by_time + bipartite_projection_by_time + line_graph_projection_by_time + dual_hypergraph_projection_by_time +Networkx Utils +~~~~~~~~~~~~~~ +.. currentmodule:: ash_model.utils.networkx +.. autosummary:: + :toctree: _autosummary/utils + :nosignatures: -------------------- -Undirected Matrices -------------------- + from_networkx_graph + from_networkx_graph_list + from_networkx_maximal_cliques + from_networkx_maximal_cliques_list + from_networkx_bipartite + from_networkx_bipartite_list -.. automodule:: ash_model.utils - :members: +Profile Utils +~~~~~~~~~~~~~ +.. currentmodule:: ash_model.utils.profiles .. autosummary:: - :toctree: utils/ + :toctree: _autosummary/utils + :nosignatures: + + aggregate_node_profile + hyperedge_most_frequent_node_attribute_value + hyperedge_aggregate_node_profile + + + +Details +------- - get_node_mapping - get_hyperedge_id_mapping - get_incidence_matrix - get_hyperedge_weight_matrix - get_vertex_degree_matrix +.. automodule:: ash_model.utils.matrices + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: +.. automodule:: ash_model.utils.networkx + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: +.. automodule:: ash_model.utils.profiles + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: +.. automodule:: ash_model.utils.projections + :members: + :undoc-members: + :inherited-members: + :show-inheritance: + :no-index: diff --git a/docs/reference/viz.rst b/docs/reference/viz.rst old mode 100644 new mode 100755 index eaed3f5..62e791f --- a/docs/reference/viz.rst +++ b/docs/reference/viz.rst @@ -1,29 +1,25 @@ -================ -Visual Analytics -================ +Visualization +============= -.. automodule:: ash_model.viz - :members: +The ``ash_model.viz`` module provides functions for visualizing hypergraph properties, +both for static snapshots and temporal evolution. ------- -Static ------- +Static Plots +------------ -.. autosummary:: - :toctree: viz/ +Functions for visualizing static hypergraph properties. - plot_s_degrees - plot_hyperedge_size_distribution - plot_degree_distribution - plot_s_ranks +.. automodule:: ash_model.viz.static + :members: + :undoc-members: + :show-inheritance: -------- -Dynamic -------- +Temporal Plots +-------------- -.. autosummary:: - :toctree: viz/ +Functions for visualizing temporal dynamics and evolution of hypergraphs. - plot_structure_dynamics - plot_attribute_dynamics - plot_consistency \ No newline at end of file +.. automodule:: ash_model.viz.temporal + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/requirements.txt b/docs/requirements.txt new file mode 100644 index 0000000..e32cb0b --- /dev/null +++ b/docs/requirements.txt @@ -0,0 +1,10 @@ +sphinx>=4.0 +furo +nbsphinx>=0.8.0 +pypandoc-binary +ipykernel +jupyter +numpy<2.0 +networkx +scipy +matplotlib diff --git a/docs/tutorial.rst b/docs/tutorial.rst old mode 100644 new mode 100755 index d93a869..3256c8d --- a/docs/tutorial.rst +++ b/docs/tutorial.rst @@ -2,328 +2,64 @@ Tutorial *************** -In this tutorial we will introduce the ``ASH`` object that can be used to describe undirected, temporal hypergraphs with attributes on nodes. +This section provides interactive tutorials to help you get started with ASH (Attributed Stream Hypergraph). +Each tutorial is a Jupyter notebook that demonstrates different aspects of the library. -Creating an ASH ----------------- +All tutorial notebooks are available in the `tutorial/ `_ folder of the repository. -Create an empty ASH with no nodes and no edges. +.. toctree:: + :maxdepth: 2 + :caption: Tutorial Notebooks -.. code:: python + tutorial/00-basics + tutorial/01-attribute_analysis + tutorial/02-walks + tutorial/03-generators + tutorial/04-io + tutorial/05-multiego + tutorial/06-segregation - from ash_model import ASH - h = ASH(hedge_removal=True) +Getting Started +--------------- -During the construction phase the ``hedge_removal`` parameter allows to specify if the structure will allow hyperedge removal or not. +The tutorials are organized in a progressive manner: +1. **Basics** (``00-basics.ipynb``): Learn how to create an ASH object, add nodes and hyperedges, and access basic properties and measures. -High-order Interactions: Hyperedges ------------------------------------ +2. **Attribute Analysis** (``01-attribute_analysis.ipynb``): Explore purity/entropy measures on hyperedge profiles, homogeneity, and temporal consistency of attributes. -``h`` can be grown by adding one interaction (i.e., an hyperedge) at a time. -Each interaction is univocally defined by an arbitrarily-large set of nodes, and has a ``start`` and a ``end`` timestamp, indicating its appearance and disappearance times respectively. +3. **Walks** (``02-walks.ipynb``): Understand s-walks, distances, and s-based components in the temporal context. -.. code:: python +4. **Generators** (``03-generators.ipynb``): Generate random hypergraphs and transform external structures into ASH objects. - h.add_hyperedge({1,2,3,4}, start=0, end=1) +5. **I/O Operations** (``04-io.ipynb``): Read and write ASH structures in various formats including CSV profiles, JSON, and HIF format. +6. **Multi-Ego Networks** (``05-multiego.ipynb``): Work with multi-ego network extraction and analysis. -If nodes are not already present in the ASH, they will be automatically added when they appear in an interaction. -In the above example the interaction ``{1,2,3,4}`` appears at time ``0`` and vanishes at time ``1``, thus being present in both timestamps. -If the ``end`` parameter is omitted, the hyperedge will only be active in ``start``. -Moreover, hyperedges are associated with a unique ``str`` identifier of the form "en" where n is a positive number: +7. **Segregation Analysis** (``06-segregation.ipynb``): Measure and analyze segregation patterns in attributed hypergraphs. -.. code:: python +Running the Notebooks +--------------------- - h.get_hyperedge_id_set() +To run the tutorial notebooks locally: - >>> {"e1"} +1. Clone the repository: + .. code-block:: bash -Multiple interactions can be added at the same time: in such scenario all the interactions in the list will have the same appearance and disappearance times. + git clone https://github.com/GiulioRossetti/ASH.git + cd ASH -.. code:: python +2. Install the required dependencies: - h.add_hyperedges([{1,2,3}, {2, 3}, {3, 1, 4}], start=1, end=2) - -The same method can be used to add any ``ebunch`` of interaction. An *ebunch* is any iterable container of interactions. - -.. code:: python - - import networkx as nx - g = nx.barabasi_albert_graph(n=500, m=3) - h.add_hyperedges(nx.find_cliques(g), start=0) - -One of the factors that make ``ash`` faster with respect to other hypergraph libraries is the ``O(1)`` access it provides to a node's star. -That is to say that given a node is is possible to easily get the set of hyperedges it is contained in. It is also possible to conveniently restrict the result to hyperedges of a given size and/or active at a given timestamp: - -.. code:: python - - h.get_star(1) # set of ids of the hyperedges that contain node 1 - h.get_star(1, hyperedge_size=4, tid=2) # set of ids of the hyperedges that contain node 1, - # have size 4 - # and are active at time 2 - - - -Node Profiles: Enrich Your Hypergraph! --------------------------------------- - -As for hyperedges, it is also possible to add one node at a time, specifying ``start``, or ``start`` and ``end`` timestamps. -The same can be done for multiple nodes at a time, which will all have the same ``start`` and ``end`` timestamps: - -.. code:: python - - # one node at a time - h.add_node(0, start=0) - h.add_node(1, start=0, end=1) - - # multiple nodes, same time window - h.add_nodes([1,2,3], start=0) - h.add_nodes([4,5,6], start=0, end=1) - - -To incorporate the semantics on nodes, ``ash`` leverages the ``NProfile`` class. -This structure can be used to contain the attributes of a node: - -.. code:: python - - from ash_model import NProfile - profile = NProfile(node_id=1, name='Alice', party='L') # add attributes at creation - profile.add_attribute('age', 24) # add attribute with dedicated method - -Node profiles can be incorporated in the ``ASH`` when adding a new node. This allows to model change in the node attributes by adding the same node at different times with different profiles: - -.. code:: python - - profile = NProfile(node_id=1, name='Alice', party='L', age=24) - h.add_node(1, start=0, attr_dict=profile) - profile2 = NProfile(node_id=1, name='Alice', party='R', age=25) - h.add_node(1, start=1, attr_dict=profile2) - -To see all information on a node profile through time, you can use the following: - -.. code:: python - - profile = h.get_node_profile(1) - attrs = profile.get_attributes() - print(attrs) - - >>> {'t': [[0, 1]], 'name': {0: 'Alice', 1: 'Alice'}, 'party': {0: 'L', 1: 'R'}, 'age': {0: 24, 1: 25}} - - -Time Respecting s-Walks ------------------------ - -``ash_model`` integrates the s-analysis framework to generalize classic graph measures to hypergraphs, and extends it with temporal information. -In short, walks are extended to hypergraphs based on a parameter ``s``, which controls the minimum number of common nodes between subsequent hyperedges. -For instance: - -.. code:: python - - from ash_model import ASH - from ash_model import paths - - h = ASH() - h.add_hyperedge([1,2,3], start=0) # e1 - h.add_hyperedge([2,3,4], start=0) # e2 - h.add_hyperedge([4,5,6], start=0) # e3 - h.add_hyperedge([1,2,3,4,5, 6], start=0) # e4 - s = 2 - - paths.has_s_walk(h, s, "e1", "e3") - - >>> True - - paths.shortest_s_walk(h, s, "e1", "e3") - - >>> ['e1', 'e4', 'e3'] - - paths.average_s_distance(h, s=2) - - >>> 1.6666666666666667 - -For more info on the s-analysis framework please refer to the original paper. The novelty with ``ASH`` is the extension to the dynamic scenario. -This means that ``ASH`` is able to compute time-respecting s-walks. - -.. code:: python - - h = ASH() - h.add_hyperedge([1, 2, 3], 0, 4) - h.add_hyperedge([1, 4], 0, 1) - h.add_hyperedge([1, 2, 3, 4], 2, 3) - trsw = paths.time_respecting_s_walks(h, s=1, hyperedge_from='e1', hyperedge_to='e3') - - for _, ap in trsw.items(): - walks = paths.annotate_walks(ap) - print('Shortest:', walks['shortest']) - print('Foremost', walks['foremost']) - -In the above example, first we get all time respecting s-walks via ``time_respecting_s_walks()``; then we annotate each path and print the fastest and the foremost ones. -Other choices include fastest, heaviest, and all possible combinations. - -High-order Mixing Patterns --------------------------- - - -Navigating in Time ------------------- - -The timestamps associated to the hyperedges can be retrieved through: - -.. code:: python - - h.temporal_snapshots_ids() - - -Several methods return statistics about the flattened (i.e., static, aggregated) hypergraph. -To get the same statistic considering a specific timestamp, you can use the ``tid`` parameter - -.. code:: python - - h.get_number_of_nodes() # count nodes in the hypergraph - h.get_number_of_nodes(tid=3) # count nodes active at time 3 - - -Once loaded, it is possible to extract a time slice from an ``ASH``, i.e., a time-span hypergraph. - -.. code:: python - - s = h.hypergraph_temporal_slice(start=2, end=3) - -the resulting ``ASH`` stored in ``s`` will be composed by nodes and interactions existing within the time span ``[2, 3]``. - - -A dynamic hypernetwork can be also described as stream of interactions, a chronologically ordered list of interactions - -.. code:: python - - for e in h.stream_interactions(): - print(e) - -the ``stream_interactions`` method returns a generator that streams the interactions in ``h``, where ``e`` is a 3-tuple ``(tid, he_id, op)`` - - - ``tid`` is the interactions timestamp - - ``he_id`` is the id associated with the corresponding hyperedge - - ``op`` is a hyperedge creation or deletion event (respectively ``+``, ``-``) - -Visual Analytics ----------------- -``ash`` also provides a module that facilitates visualizing both static and temporal statistics. - -.. code:: python - - from ash_model import viz - from matplotlib import pyplot as plt - ax = viz.plot_hyperedge_size_distribution(h) - ax.set_title('Hyperedge size distribution') - plt.show() - -All functions here are a wrapper around either ``matplotlib`` or ``seaborn`` commands, and return the ``plt.Axes`` object associated with the plot. -You can also pass a ``**kwargs`` dictionary with ``matplotlib`` plotting parameters (e.g., ``marker``). -Since all functions return the ``plt.Axes`` object, you can customize it to your likings like the above. - - - -To facilitate visualizing time series data emerging from the ``ASH``, the library provides two methods, one for the structural features, -one for the attribute-related dynamics. Let's start with the former: - -.. code:: python - - from ash_model import measures - func = measures.average_s_local_clustering_coefficient # function to be applied to all snapshots - func_params = {'s': 2} # parameters of the function above, if any - rolling = 3 # optional rolling window size for smoothing the time series - ax = viz.plot_structure_dynamics(h, func, func_params, rolling) - ax.set_title('Number of hyperedges in time') - plt.show() - -A couple of things to note here: - - ``func`` is a ``Callable`` object that is applied to all snapshots. - - ``func_params`` allows to pass arguments to ``func``. If the only parameters of a function are ``h`` and/or ``tid``, or ``start``, and ``end``, this parameter can be ignored/set to ``None``. - - ``rolling`` is an optional parameter that is used to smooth the time series. In case you have high-resolution temporal data, it is best to set this parameter; it basically computes the mean over ``rolling`` timestamps. - -Instead, for attribute dynamics we have – you guessed it: ``plot_attribute_dynamics()`` - -.. code:: python - - attr_name = "party" # compute measure for this attribute - func = measures.average_hyperedge_profile_purity # function to be applied to all snapshots - func_params = {'by_label': True} # optional parameters of the function above - rolling = 3 # optional rolling window size for smoothing the time series - - ax = viz.plot_attribute_dynamics(h, attr_name, func, func_params, rolling) - ax.set_title('Average hyperedge purity (by label)') - plt.show() - -The main differences here is that we have to set the attribute name for which we want to compute the statistics. - -In conclusion, if you want to compare different dynamic hypernetworks, you can do something like: - -.. code:: python - - hs = [h0, h1, h2] # three different ASH instances - - attr_name = "party" # compute measure for this attribute - func = measures.average_hyperedge_profile_purity # function to be applied to all snapshots - func_params = {'by_label': True} # optional parameters of the function above - rolling = 3 # optional rolling window size for smoothing the time series - - fig, axs = plt.subplots(nrows=1, ncols=len(hs), figsize=(18, 6), sharey=True, sharex=True) - plt.subplots_adjust(hspace=0.8) - - for h, ax in zip(hs, axs.ravel()): - viz.plot_attribute_dynamics(h, attr_name, func, func_params, rolling, ax=ax) - ax.grid(alpha=.2) - - plt.suptitle('Average hyperedge purity (by label)', fontsize=32) - plt.show() - - -Reading and Writing -------------------- - -``ash`` allows to read/write hypernetworks in two ways, either: - - - from/to separate files for interactions and node profiles - - from/to a single file - - -The former format allows to read/write interactions and node profiles separately. For the hyperedges: - - -.. code:: python - - from ash_model import readwrite as io - io.write_sh_to_csv(h, filename) - h = io.read_sh_from_csv(filename) - -where each row is a tab-separated list of the form ``[nodes -> start, end]``, with ``nodes`` being the members of each interactions, and ``start, end`` the appearance-disappearance times of the interactions. -Likewise, for the profiles: - -.. code:: python - - io.write_profiles_to_csv(h, filename) - profiles = io.read_profiles_from_csv(filename) - -where each row is a comma-separated list of the form ``[node_id, tid, attr1, attr2...]``. Nodes that appear multiple times are stored as a separate row for each time they are active. -Profiles can also be stored as a jsonl file with similar structure: - -.. code:: python - - io.write_profiles_to_jsonl(h, filename) - profiles = io.read_profiles_from_jsonl(filename) - - - -The latter format encloses the whole ``ASH`` in a ``json`` file - -.. code:: python - - io.write_ash_to_json(h, filename) - h = io.read_ash_from_json(filename) + .. code-block:: bash + pip install -r requirements.txt +3. Launch Jupyter: + .. code-block:: bash + jupyter notebook tutorial/ + Or open the notebooks directly in VS Code with the Jupyter extension. diff --git a/environment.yml b/environment.yml new file mode 100644 index 0000000..e938c05 --- /dev/null +++ b/environment.yml @@ -0,0 +1,11 @@ +name: ash +channels: +- conda-forge +- defaults +dependencies: +- python>=3.9 +- numpy<2.0 +- scipy +- networkx +- tqdm +- csrgraph diff --git a/requirements.txt b/requirements.txt index 1db0b5e..6444dbf 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,8 +1,7 @@ -halp -numpy -scipy +numpy<2.0 networkx +scipy +csrgraph +tqdm matplotlib -seaborn -pandas -tqdm \ No newline at end of file +fastjsonschema \ No newline at end of file diff --git a/requirements_docs.txt b/requirements_docs.txt index fdceda8..96990f6 100644 --- a/requirements_docs.txt +++ b/requirements_docs.txt @@ -1,9 +1,7 @@ -halp numpy scipy networkx matplotlib -seaborn pandas tqdm sphinx_rtd_theme \ No newline at end of file diff --git a/setup.py b/setup.py index 5721a8c..724ac33 100644 --- a/setup.py +++ b/setup.py @@ -2,7 +2,7 @@ from codecs import open from os import path -__author__ = 'Giulio Rossetti' +__author__ = "Giulio Rossetti" __license__ = "BSD" __email__ = "giulio.rossetti@gmail.com" @@ -13,44 +13,43 @@ here = path.abspath(path.dirname(__file__)) # Get the long description from the README file -with open(path.join(here, 'README.md'), encoding='utf-8') as f: +with open(path.join(here, "README.md"), encoding="utf-8") as f: long_description = f.read() -with open(path.join(here, 'requirements.txt'), encoding='utf-8') as f: +with open(path.join(here, "requirements.txt"), encoding="utf-8") as f: requirements = f.read().splitlines() -setup(name='ash_model', - version='0.1.0', - license='BSD-Clause-2', - description='Attributed Stream Hypergraph library', - url='https://github.com/GiulioRossetti/ASH', - author='Giulio Rossetti', - author_email='giulio.rossetti@gmail.com', - classifiers=[ - # How mature is this project? Common values are - # 3 - Alpha - # 4 - Beta - # 5 - Production/Stable - 'Development Status :: 4 - Beta ', - - # Indicate who your project is intended for - 'Intended Audience :: Developers', - 'Topic :: Software Development :: Build Tools', - - # Pick your license as you wish (should match "license" above) - 'License :: OSI Approved :: GNU General Public License v3 or later (GPLv3+)', - - "Operating System :: OS Independent", - - # Specify the Python versions you support here. In particular, ensure - # that you indicate whether you support Python 2, Python 3 or both. - 'Programming Language :: Python', - 'Programming Language :: Python :: 3' - ], - keywords='dynamic-networks', - install_requires=requirements, - long_description=long_description, - long_description_content_type='text/markdown', - packages=find_packages(exclude=["*.test", "*.test.*", "test.*", "test", "ash.test", "ash.test.*"]), - ) +setup( + name="ash_model", + version="1.0.0", + license="BSD-Clause-2", + description="Attributed Stream Hypergraph library", + url="https://github.com/GiulioRossetti/ASH", + author="Giulio Rossetti", + author_email="giulio.rossetti@gmail.com", + classifiers=[ + # How mature is this project? Common values are + # 3 - Alpha + # 4 - Beta + # 5 - Production/Stable + "Development Status :: 4 - Beta ", + # Indicate who your project is intended for + "Intended Audience :: Developers", + "Topic :: Software Development :: Build Tools", + # Pick your license as you wish (should match "license" above) + "License :: OSI Approved :: GNU General Public License v3 or later (GPLv3+)", + "Operating System :: OS Independent", + # Specify the Python versions you support here. In particular, ensure + # that you indicate whether you support Python 2, Python 3 or both. + "Programming Language :: Python", + "Programming Language :: Python :: 3", + ], + keywords="dynamic-networks", + install_requires=requirements, + long_description=long_description, + long_description_content_type="text/markdown", + packages=find_packages( + exclude=["*.test", "*.test.*", "test.*", "test", "ash.test", "ash.test.*"] + ), +) diff --git a/tutorial/00-basics.ipynb b/tutorial/00-basics.ipynb new file mode 100644 index 0000000..e4d074e --- /dev/null +++ b/tutorial/00-basics.ipynb @@ -0,0 +1,1181 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5612868e", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "Author: Andrea Failla
\n", + "Python version: 3.9
\n", + "ASH version: 0.1.0
\n", + "Last update: July 2025\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "0f8cd256", + "metadata": {}, + "source": [ + "\n", + "# Attributed Stream Hypergraphs (ASH)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "id": "ccfc978d", + "metadata": {}, + "outputs": [], + "source": [ + "#!pip install -e ../" + ] + }, + { + "cell_type": "markdown", + "id": "65e2c245", + "metadata": {}, + "source": [ + "\n", + "# Table of Contents\n", + "\n", + " - [Introduction](#introduction)\n", + " - [Basic Concepts](#basic-concepts)\n", + " - [What is a Hypergraph?](#what-is-a-hypergraph)\n", + " - [What is an Attributed Stream Hypergraph?](#what-is-an-attributed-stream-hypergraph)\n", + " - [Installation](#installation)\n", + " - [Creating an ASH Instance](#creating-an-ash-instance)\n", + " - [Populating an ASH](#populating-an-ash)\n", + " - [Retrieving information from ASH](#retrieving-information-from-ash)\n", + " - [Basic analysis](#basic-analysis)\n", + "- [Node Profiles](#node-profiles)\n", + " - [Working with Statistics](#working-with-statistics)\n", + " - [An algebra of node attributes](#an-algebra-of-node-attributes)" + ] + }, + { + "cell_type": "markdown", + "id": "265d0011", + "metadata": {}, + "source": [ + "\n", + "## Introduction\n", + "\n", + "The ASH (Attributed Stream Hypergraph) is a powerful data structure for modeling temporal higher-order interactions. Unlike traditional graphs that connect pairs of nodes, hypergraphs can represent interactions among multiple entities simultaneously, and the ASH extends this concept to include temporal dynamics and rich attribute information.\n", + "\n", + "This tutorial will guide you through the core concepts and practical usage of the ASH library.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "b6e02b23", + "metadata": {}, + "source": [ + "\n", + "## Basic Concepts\n", + "\n", + "\n", + "### What is a Hypergraph?\n", + "\n", + "A hypergraph is a generalization of a graph where edges (called hyperedges) can connect any number of vertices, not just two. For example:\n", + "- In a regular graph: Alice → Bob (edge connects 2 nodes)\n", + "- In a hypergraph, apart from the case above, the following is also allowed: Alice, Bob, Charlie (hyperedge connects 3+ nodes)\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "5668c46d", + "metadata": {}, + "source": [ + "\n", + "### What is an Attributed Stream Hypergraph?\n", + "\n", + "An ASH combines three key features:\n", + "1. **Hypergraph structure**: Edges can connect multiple nodes\n", + "2. **Temporal dynamics**: Hyperedges can appear and disappear over time\n", + "3. **Rich attributes**: Both nodes and hyperedges can have attributes, which can change over time\n", + "\n", + "Consider a collaboration hypernetwork where:\n", + "- Nodes represent researchers\n", + "- Hyperedges represent papers written by two or more authors\n", + "\n", + "This setting is adequately modeled with a hypergraph, as collaborations typically go beyond pairs of authors. With ASH, you can study how these collaborations evolve over time (e.g., year after year), as well as how attributes relate to/affect changes in topology. For instance, nodes/authors can be labeled with their main institution. As this affiliation changes over time, it is likely that the researcher's opportunities for collaboration change as well.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "1363f5a8", + "metadata": {}, + "source": [ + "ASHs can easily allow for the analyses, among others, of higher-order homophily, nodes’ homophily with respect to the hyperedges in which nodes participate, and time-respecting paths between hyperedges." + ] + }, + { + "cell_type": "markdown", + "id": "01327193", + "metadata": {}, + "source": [ + "\n", + "## Installation\n", + "First, let's install the library. The easiest way to do so is via pip:\n", + "\n", + " pip install ash_model \n", + "\n", + "Then we can check that the library is installed by importing it:\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a99277f5", + "metadata": {}, + "outputs": [], + "source": [ + "import ash_model" + ] + }, + { + "cell_type": "markdown", + "id": "fda786ec", + "metadata": {}, + "source": [ + "\n", + "## Creating an ASH Instance\n", + "The library has two main classes that users can interact with: \n", + "- **ASH**, to create, manipulate, and work with attributed temporal hypergraphs\n", + "- **NProfile**, which is a high-level structure to model nodes and their attributes.\n", + "\n", + "To instantiate an ASH, simply do:\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d9620b6a", + "metadata": {}, + "outputs": [], + "source": [ + "from ash_model import ASH\n", + "ash = ASH()" + ] + }, + { + "cell_type": "markdown", + "id": "103df6ab", + "metadata": {}, + "source": [ + "### Backend Selection\n", + "\n", + "Since it is designed to work with complex temporal data, ASH offers two storage backends with different performance characteristics:\n", + "\n", + "| Backend | Storage | Best For | Complexity |\n", + "|---------|---------|----------|------------|\n", + "| **Dense** (default) | time → set(hyperedge_ids) | Dense timelines, frequent snapshot queries | materialise: O(1), add: O(1) |\n", + "| **Interval** | hyperedge_id → [(start, end)] | Sparse temporal data, long-lived entities | materialise: O(N×log k), add: O(1) |\n", + "\n", + "**Usage:**\n", + "\n", + "```python\n", + "# Dense backend (default) - best for frequent queries\n", + "ash_dense = ASH()\n", + "\n", + "# Interval backend - best for sparse temporal networks\n", + "ash_interval = ASH(backend=\"interval\")\n", + "```\n", + "\n", + "**When to use Interval backend:**\n", + "- Working with long-lived entities or hyperedges\n", + "- Sparse temporal data (few active times per entity)\n", + "- Memory-constrained environments\n", + "- Fewer snapshot queries compared to updates\n", + "\n", + "**Technical Note:** \n", + "The Interval backend uses two key optimizations:\n", + "1. **Binary search (bisect)**: O(log k) lookup per entity instead of O(k) linear scan, where k is the average number of intervals per entity\n", + "2. **Event-difference arrays**: O(1) updates for interval additions/removals using difference arrays, avoiding O(length) per-time loops\n", + "\n", + "These optimizations provide ~10x performance improvements for interval-based operations while maintaining identical output to the Dense backend." + ] + }, + { + "cell_type": "markdown", + "id": "47dedf15", + "metadata": {}, + "source": [ + "\n", + "## Populating an ASH\n", + "You can add nodes to an ASH by using the corresponding methods:\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "cceafa5d", + "metadata": {}, + "outputs": [], + "source": [ + "# Add a node present from time 0 to 5 (inclusive)\n", + "ash.add_node(node=1, start=0, end=5)\n", + "\n", + "# Add a single node at time 0\n", + "ash.add_node(node=2, start=0) # This node is present at time 0 only\n", + "\n", + "# Add a node with attributes\n", + "ash.add_node(node=3, start=0, end=2, attr_dict={\"name\": \"Alice\", \"age\": 25})" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9d484803", + "metadata": {}, + "outputs": [], + "source": [ + "# Add multiple nodes at once\n", + "ash.add_nodes(nodes=[4, 5, 6], start=0, end=3)\n", + "\n", + "# Add nodes with different attributes\n", + "node_attrs = {\n", + " 4: {\"name\": \"Bob\", \"department\": \"CS\"},\n", + " 5: {\"name\": \"Charlie\", \"department\": \"Math\"},\n", + " 6: {\"name\": \"Diana\", \"department\": \"Physics\"}\n", + "}\n", + "\n", + "# this overrides the previous nodes\n", + "ash.add_nodes(nodes=[4, 5, 6], start=0, end=3, node_attr_dict=node_attrs)" + ] + }, + { + "cell_type": "markdown", + "id": "3b76f2e3", + "metadata": {}, + "source": [ + "A couple of things to note here:\n", + "- Most methods in ash have start and end parameters specifying temporal bounds. Both of these extremes are inclusive.\n", + "- Adding the same node(s) at times where it is already present overrides the previous configuration\n", + "- Adding the same node(s) to multiple time windows can be done by calling add_node() with the same node_id and different start and end parameters.\n", + "\n", + "Adding hyperedges follows the same logic, it is as easy as:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "3732f948", + "metadata": {}, + "outputs": [], + "source": [ + "# Add a hyperedge connecting nodes 1, 2, 3 at time 0\n", + "ash.add_hyperedge(nodes=[1, 2, 3], start=0)\n", + "\n", + "# Add a hyperedge present from time 0 to 2\n", + "ash.add_hyperedge(nodes=[2, 3, 4], start=0, end=2)\n", + "\n", + "# Add a hyperedge with attributes\n", + "ash.add_hyperedge(nodes=[1, 4, 5], start=1, end=3, weight=2.5, type=\"collaboration\")\n", + "\n", + "# Add multiple hyperedges with same time span\n", + "hyperedges = [[1, 2], [3, 4], [5, 6]]\n", + "ash.add_hyperedges(hyperedges, start=0, end=1, type=\"communication\")" + ] + }, + { + "cell_type": "markdown", + "id": "2ca56fc4", + "metadata": {}, + "source": [ + "Similarly, nodes and hyperedges can be removed. This is often computationally expensive, so it is advised to use these operations sparingly and only when necessary." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "0b9add36", + "metadata": {}, + "outputs": [], + "source": [ + "# remove a hyperedge over all time spans\n", + "# ash.remove_hyperedge('e1')\n", + "\n", + "# remove a node from a specific time span\n", + "# ash.remove_node(node=1, start=3)\n", + "\n", + "# similarly, can remove in batch\n", + "# ash.remove_nodes(nodes=[2, 3], start=0, end=2)\n", + "# ash.remove_hyperedges(hyperedges=['e3', 'e2'], start=0, end=1)" + ] + }, + { + "cell_type": "markdown", + "id": "b5490477", + "metadata": {}, + "source": [ + "\n", + "## Retrieving information from ASH\n", + "Once an ASH is built, you can use some utilities to retrieve information from it. To access the times where it is active:\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "b501509b", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 1, 2, 3, 4, 5]" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ash.temporal_snapshots_ids()" + ] + }, + { + "cell_type": "markdown", + "id": "03efeb56", + "metadata": {}, + "source": [ + "To access nodes:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "b98c923d", + "metadata": {}, + "outputs": [], + "source": [ + "for node in ash.nodes():\n", + " # cycle through all nodes\n", + " pass\n", + "for node in ash.nodes(start=0, end=3):\n", + " # cycle through nodes present at time 0 to 3\n", + " pass" + ] + }, + { + "cell_type": "markdown", + "id": "93530bb3", + "metadata": {}, + "source": [ + "To access edges:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "b87f15b9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "e5\n", + "e4\n", + "e6\n" + ] + } + ], + "source": [ + "for he in ash.hyperedges():\n", + " # cycle through all hyperedges\n", + " pass\n", + "for he in ash.hyperedges(start=0):\n", + " # cycle through hyperedges present at time 0\n", + " pass\n", + "for he in ash.hyperedges(hyperedge_size=2):\n", + " # cycle through hyperedges with size 2\n", + " print(he)" + ] + }, + { + "cell_type": "markdown", + "id": "dacf4dfd", + "metadata": {}, + "source": [ + "As you can see, hyperedges are assigned a hyperedge id (string) at creation. To retrieve the actual sets of nodes you can do:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "749004e6", + "metadata": {}, + "outputs": [], + "source": [ + "for he in ash.hyperedges(as_ids=False):\n", + " pass\n", + " \n", + "# or \n", + "he_nodes = ash.get_hyperedge_nodes('e1') \n", + "\n", + "# conversely, to get the hyperedge id from a set of nodes:\n", + "he_id = ash.get_hyperedge_id(nodes=[1, 2, 3])" + ] + }, + { + "cell_type": "markdown", + "id": "79335280", + "metadata": {}, + "source": [ + "You can also stream all interactions. This yields activation and deactivation times of all edges:" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "349943cb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Time 0: Hyperedge e5 was +\n", + "Time 0: Hyperedge e2 was +\n", + "Time 0: Hyperedge e4 was +\n", + "Time 0: Hyperedge e6 was +\n", + "Time 0: Hyperedge e1 was +\n", + "Time 1: Hyperedge e3 was +\n", + "Time 1: Hyperedge e1 was -\n", + "Time 2: Hyperedge e5 was -\n", + "Time 2: Hyperedge e4 was -\n", + "Time 2: Hyperedge e6 was -\n", + "Time 3: Hyperedge e2 was -\n", + "Time 4: Hyperedge e3 was -\n" + ] + } + ], + "source": [ + "for time, hedge_id, event in ash.stream_interactions():\n", + " print(f\"Time {time}: Hyperedge {hedge_id} was {event}\")" + ] + }, + { + "cell_type": "markdown", + "id": "fecbfaa2", + "metadata": {}, + "source": [ + "Finally, you can check node and hyperedge presence at specific times:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "97117cc1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Node 1 exists in time range [0,2]: True\n", + "Hyperedge [1,2,3] exists at time 1: False\n" + ] + } + ], + "source": [ + "# Check if node exists\n", + "has_node = ash.has_node(1, start=0, end=2)\n", + "print(f\"Node 1 exists in time range [0,2]: {has_node}\")\n", + "\n", + "# Check if hyperedge exists\n", + "has_hyperedge = ash.has_hyperedge([1, 2, 3], start=1)\n", + "print(f\"Hyperedge [1,2,3] exists at time 1: {has_hyperedge}\")" + ] + }, + { + "cell_type": "markdown", + "id": "534ad55d", + "metadata": {}, + "source": [ + "In general, to get a specific node/hyperedge's temporal presence:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "66354f0a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Node 1 present at times: [0, 1, 2, 3, 4, 5]\n", + "Node 1 present in intervals: [(0, 5)]\n", + "Hyperedge present in intervals: [(0, 0)]\n" + ] + } + ], + "source": [ + "# Get presence of a node over time\n", + "node_presence = ash.node_presence(1)\n", + "print(f\"Node 1 present at times: {node_presence}\")\n", + "\n", + "# Get presence as intervals\n", + "node_intervals = ash.node_presence(1, as_intervals=True)\n", + "print(f\"Node 1 present in intervals: {node_intervals}\")\n", + "\n", + "# Hyperedge presence\n", + "hedge_id = ash.get_hyperedge_id([1, 2, 3])\n", + "hedge_presence = ash.hyperedge_presence(hedge_id, as_intervals=True)\n", + "print(f\"Hyperedge present in intervals: {hedge_presence}\")" + ] + }, + { + "cell_type": "markdown", + "id": "cd63f1bf", + "metadata": {}, + "source": [ + "To retrieve information about attributes:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "50746fdf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Node attributes: {'name': {'Alice', 'Bob', 'Diana', 'Charlie'}, 'age': {25}, 'department': {'Math', 'CS', 'Physics'}}\n", + "Hyperedge attributes: {'type': {'communication', 'collaboration'}, 'weight': {1, 2.5}}\n", + "Node 5 attributes: {0: {'name': 'Charlie', 'department': 'Math'}, 1: {'name': 'Charlie', 'department': 'Math'}, 2: {'name': 'Charlie', 'department': 'Math'}, 3: {'name': 'Charlie', 'department': 'Math'}}\n", + "Hyperedge attributes: {'weight': 1}\n" + ] + } + ], + "source": [ + "n_attrs = ash.list_node_attributes()\n", + "he_attrs = ash.list_hyperedge_attributes()\n", + "print(f\"Node attributes: {n_attrs}\")\n", + "print(f\"Hyperedge attributes: {he_attrs}\")\n", + "\n", + "# Get node attributes\n", + "node_attrs = ash.get_node_attributes(5)\n", + "print(f\"Node 5 attributes: {node_attrs}\")\n", + "\n", + "# Get hyperedge attributes\n", + "he_attrs = ash.get_hyperedge_attributes('e1')\n", + "print(f\"Hyperedge attributes: {he_attrs}\")" + ] + }, + { + "cell_type": "markdown", + "id": "d69c10f0", + "metadata": {}, + "source": [ + "> **Note**: further information about handling node attributes is given in the Node Profile section below" + ] + }, + { + "cell_type": "markdown", + "id": "f2e00ed7", + "metadata": {}, + "source": [ + "\n", + "## Basic analysis\n", + "Here are some commonly used commands to extract information from ASH instances.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "5991dada", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Node 1's star: ['e3', 'e4', 'e1']\n", + "Node 1's degree: 3\n", + "Node 1's neighbors: {2, 3, 4, 5}\n", + "Node 1's degree by size: {3: 2, 2: 1}\n" + ] + } + ], + "source": [ + "# Get node's star (all hyperedges containing the node)\n", + "star = ash.star(1, start=0, end=2)\n", + "print(f\"Node 1's star: {star}\")\n", + "\n", + "# Get node degree\n", + "degree = ash.degree(1, start=0, end=2)\n", + "print(f\"Node 1's degree: {degree}\")\n", + "\n", + "# Get neighbors\n", + "neighbors = ash.neighbors(1, start=0, end=2)\n", + "print(f\"Node 1's neighbors: {neighbors}\")\n", + "\n", + "# Degree by hyperedge size\n", + "degree_by_size = ash.degree_by_hyperedge_size(1, start=0, end=2)\n", + "print(f\"Node 1's degree by size: {degree_by_size}\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "fe311d5f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of nodes: 6\n", + "Number of hyperedges: 6\n", + "Hyperedge size distribution: {2: 3, 3: 3}\n", + "Degree distribution: {3: 4, 2: 1, 1: 1}\n" + ] + } + ], + "source": [ + "# Network size\n", + "print(f\"Number of nodes: {ash.number_of_nodes()}\")\n", + "print(f\"Number of hyperedges: {ash.number_of_hyperedges()}\")\n", + "\n", + "# Size distributions\n", + "hedge_size_dist = ash.hyperedge_size_distribution()\n", + "print(f\"Hyperedge size distribution: {hedge_size_dist}\")\n", + "\n", + "degree_dist = ash.degree_distribution()\n", + "print(f\"Degree distribution: {degree_dist}\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "1bdab8ef", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Average nodes per snapshot: 4.00\n", + "Average hyperedges per snapshot: 2.17\n", + "Coverage: 0.67\n", + "Uniformity: 0.74\n", + "Node 1 contribution: 1.00\n", + "Hyperedge e1 contribution: 0.17\n" + ] + } + ], + "source": [ + "# Average statistics over time\n", + "avg_nodes = ash.avg_number_of_nodes()\n", + "avg_hyperedges = ash.avg_number_of_hyperedges()\n", + "\n", + "print(f\"Average nodes per snapshot: {avg_nodes:.2f}\")\n", + "print(f\"Average hyperedges per snapshot: {avg_hyperedges:.2f}\")\n", + "\n", + "# Coverage and uniformity\n", + "coverage = ash.coverage()\n", + "uniformity = ash.uniformity()\n", + "\n", + "print(f\"Coverage: {coverage:.2f}\")\n", + "print(f\"Uniformity: {uniformity:.2f}\")\n", + "\n", + "# Node contribution (fraction of time present)\n", + "node_contrib = ash.node_contribution(1)\n", + "print(f\"Node 1 contribution: {node_contrib:.2f}\")\n", + "\n", + "# Hyperedge contribution\n", + "hedge_contrib = ash.hyperedge_contribution(hedge_id)\n", + "print(f\"Hyperedge {hedge_id} contribution: {hedge_contrib:.2f}\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9702e083", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "85bc4a97", + "metadata": {}, + "source": [ + "\n", + "# Node Profiles\n", + "\n", + "The `NProfile` class is a high-level structure designed to model nodes and their attributes within the ASH framework. It provides a flexible way to store, manage, and analyze node attributes along with computed statistics.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "3e54013e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Attribute name: Edward\n", + "Attribute age: 25\n", + "Attribute department: Math\n" + ] + } + ], + "source": [ + "from ash_model import NProfile\n", + "\n", + "# Create a profile without attributes and tie to a node ID\n", + "profile = NProfile(node_id=7)\n", + "\n", + "# Create a profile with initial attributes\n", + "profile = NProfile(node_id=7, name=\"Edward\", age=25, department=\"Math\")\n", + "profile2 = NProfile(node_id=7, name=\"Edward\", age=26, department=\"Math\")\n", + "profile3 = NProfile(node_id=7, name=\"Edward\", age=27, department=\"Physics\")\n", + "\n", + "for attr_name, attr_value in profile.items():\n", + " print(f\"Attribute {attr_name}: {attr_value}\")" + ] + }, + { + "cell_type": "markdown", + "id": "27fdd72d", + "metadata": {}, + "source": [ + "This profile can then be added to the ASH and retrieved subsequently" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "ce280be4", + "metadata": {}, + "outputs": [], + "source": [ + "ash.add_node(node=7, start=0, attr_dict=profile)\n", + "ash.add_node(node=7, start=1, attr_dict=profile2)\n", + "ash.add_node(node=7, start=2, attr_dict=profile3)" + ] + }, + { + "cell_type": "markdown", + "id": "d3f5f508", + "metadata": {}, + "source": [ + "To get the profile of a node at a specific time, simply do:" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "1b6b497c", + "metadata": {}, + "outputs": [], + "source": [ + "profile_t1 = ash.get_node_profile(7, tid=1) # Retrieve the profile for node 7 at time 1" + ] + }, + { + "cell_type": "markdown", + "id": "7363a291", + "metadata": {}, + "source": [ + "If you do not pass the tid parameter, an aggregated node profile is returned, where numerical values are averaged, and categorical values are substituted with the most frequent one." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "862956a4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'name': 'Edward', 'age': 26.0, 'department': 'Math'}" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "aggregated_profile = ash.get_node_profile(7) # Retrieve the aggregated profile for node 7\n", + "aggregated_profile.get_attributes() # Get all attributes of the profile" + ] + }, + { + "cell_type": "markdown", + "id": "7e653ce4", + "metadata": {}, + "source": [ + "In case you need to access all profiles of a node over time:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "c37132b4", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: ,\n", + " 1: ,\n", + " 2: }" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ash.get_node_profiles_by_time(7) # Get all profiles of node 7 over time" + ] + }, + { + "cell_type": "markdown", + "id": "f5b08b8f", + "metadata": {}, + "source": [ + "\n", + "## Working with Statistics\n", + "\n", + "One of the key features of `NProfile` is the ability to store computed statistics for attributes. This is particularly useful for temporal analysis where you might want to track how attributes change over time.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "1b278db9", + "metadata": {}, + "outputs": [], + "source": [ + "profile = NProfile(node_id=1, name=\"Alice\", age=25, department=\"CS\")\n", + "# First, ensure the attribute exists\n", + "profile.add_attribute(\"publications\", 15)\n", + "\n", + "# Add statistics for the publications attribute\n", + "profile.add_statistic(\"publications\", \"mean\", 12.5)\n", + "profile.add_statistic(\"publications\", \"max\", 20)\n", + "profile.add_statistic(\"publications\", \"min\", 5)\n", + "profile.add_statistic(\"publications\", \"std\", 3.2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "631c2951", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{'mean': 12.5, 'max': 20, 'min': 5, 'std': 3.2}\n", + "{'mean': 12.5}\n", + "Has median: False\n", + "['mean', 'max', 'min', 'std']\n" + ] + } + ], + "source": [ + "# Get all statistics for an attribute\n", + "pub_stats = profile.get_statistic(\"publications\")\n", + "print(pub_stats) # Output: {'mean': 12.5, 'max': 20, 'min': 5, 'std': 3.2}\n", + "\n", + "# Get a specific statistic\n", + "mean_pubs = profile.get_statistic(\"publications\", \"mean\")\n", + "print(mean_pubs) # Output: {'mean': 12.5}\n", + "\n", + "# Check if a statistic exists\n", + "has_median = profile.has_statistic(\"publications\", \"median\")\n", + "print(f\"Has median: {has_median}\") # Output: Has median: False\n", + "\n", + "# List all computed statistics for an attribute\n", + "stat_names = profile.attribute_computed_statistics(\"publications\")\n", + "print(stat_names) # Output: ['mean', 'max', 'min', 'std']" + ] + }, + { + "cell_type": "markdown", + "id": "2d729af7", + "metadata": {}, + "source": [ + "\n", + "## An algebra of node attributes\n", + "`NProfile` objects can be compared using standard Python comparison operators:\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "cb779055", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True\n", + "False\n" + ] + } + ], + "source": [ + "# Create two profiles with same attributes\n", + "profile1 = NProfile(node_id=1, name=\"Alice\", age=25)\n", + "profile2 = NProfile(node_id=2, name=\"Alice\", age=25)\n", + "\n", + "# Equality is based on attributes, not node_id\n", + "print(profile1 == profile2) # Output: True\n", + "\n", + "# Different attributes\n", + "profile3 = NProfile(node_id=1, name=\"Alice\", age=30)\n", + "print(profile1 == profile3) # Output: False" + ] + }, + { + "cell_type": "markdown", + "id": "18e2ee47", + "metadata": {}, + "source": [ + "For profiles with numeric attributes, you can use `>=` and `<=` operators:" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "832f4a56", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True\n", + "True\n" + ] + } + ], + "source": [ + "# Create profiles with numeric attributes\n", + "researcher1 = NProfile(publications=10, citations=150, h_index=8)\n", + "researcher2 = NProfile(publications=8, citations=120, h_index=6)\n", + "\n", + "# Check if researcher1 has >= values in all numeric attributes\n", + "print(researcher1 >= researcher2) # Output: True\n", + "\n", + "# Check if researcher2 has <= values in all numeric attributes\n", + "print(researcher2 <= researcher1) # Output: True\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "8f903004", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Attributed Stream Hypergraph\n", + "Nodes: 100\n", + "Hyperedges: 8101\n", + "Snapshots: 30\n", + "Node attributes: \n", + "\n" + ] + } + ], + "source": [ + "from ash_model import viz\n", + "\n", + "import networkx as nx\n", + "from ash_model import ASH\n", + "from ash_model.utils import from_networkx_maximal_cliques_list\n", + "\n", + "snapshots = [nx.barabasi_albert_graph(100, 5) for _ in range(30)]\n", + "ash = from_networkx_maximal_cliques_list(snapshots)\n", + "print(ash)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "f9020a4f", + "metadata": {}, + "outputs": [], + "source": [ + "from ash_model.viz.temporal import plot_node_activity_series, plot_hyperedge_activity_series, plot_presence_timeline, plot_inter_event_time_distribution, plot_hyperedge_lifespan_distribution, plot_node_lifespan_distribution\n" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "56c9cc01", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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", 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", 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", 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "%matplotlib inline\n", + "\n", + "plt.show()\n", + "plot_node_activity_series(ash)\n", + "plt.show()\n", + "plot_hyperedge_activity_series(ash)\n", + "plt.show()\n", + "plot_presence_timeline(ash, nodes=[1,2,3])\n", + "plt.show()\n", + "plot_presence_timeline(ash, hyperedges=['e1', 'e2', 'e3'])\n", + "plt.show()\n", + "plot_inter_event_time_distribution(ash)\n", + "plt.show()\n", + "plot_hyperedge_lifespan_distribution(ash)\n", + "plt.show()\n", + "plot_node_lifespan_distribution(ash)\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9614226f", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.20" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/01-attribute_analysis.ipynb b/tutorial/01-attribute_analysis.ipynb new file mode 100644 index 0000000..31a0a4c --- /dev/null +++ b/tutorial/01-attribute_analysis.ipynb @@ -0,0 +1,385 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "5c2827c5", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "Author: Andrea Failla
\n", + "Python version: 3.9
\n", + "ASH version: 0.1.0
\n", + "Last update: July 2025\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "b14f1f3a", + "metadata": {}, + "source": [ + "\n", + "# Attributed Stream Hypergraphs (ASH)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "cbef6d81", + "metadata": {}, + "outputs": [], + "source": [ + "#!pip install -e ../" + ] + }, + { + "cell_type": "markdown", + "id": "1fdde502", + "metadata": {}, + "source": [ + "\n", + "# Table of Contents\n", + "\n", + "- [Introduction](#introduction)\n", + "- [Hyperedge-Level Measures](#hyperedge-level-measures)\n", + " - [Purity of Hyperedge Profiles](#purity-of-hyperedge-profiles)\n", + " - [Entropy of Hyperedge Profiles](#entropy-of-hyperedge-profiles)\n", + "- [Star-Level Measures](#star-level-measures)\n", + " - [Star Profile Entropy](#star-profile-entropy)\n", + " - [Star Profile Homogeneity](#star-profile-homogeneity)\n", + "- [Group-Level Measures: Average Group Degree](#group-level-measures-average-group-degree)\n", + "- [Temporal Consistency of Attributes](#temporal-consistency-of-attributes)\n" + ] + }, + { + "cell_type": "markdown", + "id": "97783a89", + "metadata": {}, + "source": [ + "\n", + "## Introduction\n", + "\n", + "This tutorial will guide you through some functionalities offered by ASH to analyze properties related to node attributes.\n", + "\n", + "All methods in this module share the following characteristics:\n", + "1. They return results for all attributes;\n", + "2. Their return type is a dictionary, typically containing the attribute name (or value) and the corresponding score;\n", + "3. Imternally, they process NProfile objects. If you are not familiar with them, see the corresponding section in the \"basics\" tutorial notebook.\n", + "\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "ad610055", + "metadata": {}, + "outputs": [], + "source": [ + "# Import necessary libraries\n", + "import networkx as nx\n", + "from ash_model.utils import from_networkx_maximal_cliques_list\n", + "from ash_model.measures import (\n", + " hyperedge_profile_purity,\n", + " hyperedge_profile_entropy,\n", + " star_profile_entropy,\n", + " star_profile_homogeneity,\n", + " average_group_degree,\n", + " attribute_consistency\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "b645cc4b", + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "snapshots = []\n", + "for _ in range(10):\n", + " g = nx.barabasi_albert_graph(100, 5)\n", + " for node in g.nodes:\n", + " g.nodes[node]['color'] = random.choice(['red', 'blue', 'green', 'yellow'])\n", + " g.nodes[node]['role'] = random.choice(['admin', 'user', 'guest'])\n", + " g.nodes[node]['team'] = random.choice(['engineering', 'marketing', 'sales'])\n", + " snapshots.append(g)\n", + "ash = from_networkx_maximal_cliques_list(snapshots)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d8298d51", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'color': {'blue', 'green', 'red', 'yellow'},\n", + " 'role': {'admin', 'guest', 'user'},\n", + " 'team': {'engineering', 'marketing', 'sales'}}" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# the maximal cliques method preserves the attributes\n", + "ash.list_node_attributes()" + ] + }, + { + "cell_type": "markdown", + "id": "fb904a21", + "metadata": {}, + "source": [ + "## 2. Hyperedge-Level Measures\n", + "\n", + "### 2.1 Purity of Hyperedge Profiles\n", + "\n", + "Purity measures the dominance of the most frequent attribute value among\n", + "the nodes in a hyperedge. A purity score of 1.0 means all nodes share\n", + "the same attribute value." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "1992ec3c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Purity per attribute: {'role': {'user': 0.6666666666666666}, 'color': {'blue': 1.0}, 'team': {'marketing': 0.6666666666666666}}\n" + ] + } + ], + "source": [ + "# Example: compute purity for hyperedge 'e42' at time tid=0\n", + "purity = hyperedge_profile_purity(ash, hyperedge_id='e1', tid=0)\n", + "print(\"Purity per attribute:\", purity)\n" + ] + }, + { + "cell_type": "markdown", + "id": "be87b544", + "metadata": {}, + "source": [ + "### 2.2 Entropy of Hyperedge Profiles\n", + "\n", + "Entropy quantifies the diversity of attribute values. Higher entropy\n", + "indicates more variety.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "6837dc07", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Entropy per attribute: {'color': 0, 'role': 0.9182958340544896, 'team': 0.9182958340544896}\n" + ] + } + ], + "source": [ + "entropy = hyperedge_profile_entropy(ash, hyperedge_id='e1', tid=0)\n", + "print(\"Entropy per attribute:\", entropy)\n" + ] + }, + { + "cell_type": "markdown", + "id": "d5232ed8", + "metadata": {}, + "source": [ + "## 3. Star-Level Measures\n", + "\n", + "The **star** of a node is the set of hyperedges in which it\n", + "participates. We can analyze attribute distributions across its\n", + "neighborhood.\n", + "\n", + "### 3.1 Star Profile Entropy\n", + "\n", + "Compute attribute entropy across either the aggregated hyperedge\n", + "profiles (`method='aggregate'`) or directly across neighbors\n", + "(`method='collapse'`)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "84bb9356", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Star entropy (aggregate): {'color': 0.5205045904698237, 'role': 0.38189623095230185, 'team': 0.918555783726957}\n", + "Star entropy (collapse): {'color': 0.8425589668297178, 'role': 0.9659535505394683, 'team': 0.998252681697666}\n" + ] + } + ], + "source": [ + "# Using aggregate method\n", + "star_ent_agg = star_profile_entropy(ash, node_id=10, tid=0, method='aggregate')\n", + "print(\"Star entropy (aggregate):\", star_ent_agg)\n", + "\n", + "# Using collapse method\n", + "star_ent_col = star_profile_entropy(ash, node_id=10, tid=0, method='collapse')\n", + "print(\"Star entropy (collapse):\", star_ent_col)" + ] + }, + { + "cell_type": "markdown", + "id": "5480dcfe", + "metadata": {}, + "source": [ + "### 3.2 Star Profile Homogeneity\n", + "\n", + "Homogeneity measures how aligned the neighbors are with the focal node’s\n", + "attribute values." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "8a5189d3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Star homogeneity: {'color': 0.8148148148148148, 'role': 0.8888888888888888, 'team': 0.4074074074074074}\n" + ] + } + ], + "source": [ + "star_homog = star_profile_homogeneity(ash, node_id=10, tid=0, method='aggregate')\n", + "print(\"Star homogeneity:\", star_homog)" + ] + }, + { + "cell_type": "markdown", + "id": "496799e3", + "metadata": {}, + "source": [ + "## 4. Group-Level Measures: Average Group Degree\n", + "\n", + "This function computes, for each categorical attribute, the average\n", + "hyperedge-degree of nodes sharing each attribute value.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "9a75c3f7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Attribute 'color':\n", + " yellow: 6.89\n", + " blue: 9.69\n", + " red: 10.71\n", + " green: 8.21\n", + "Attribute 'role':\n", + " user: 9.14\n", + " admin: 7.62\n", + " guest: 10.16\n", + "Attribute 'team':\n", + " engineering: 7.90\n", + " marketing: 7.81\n", + " sales: 10.71\n" + ] + } + ], + "source": [ + "avg_deg = average_group_degree(ash, tid=0, hyperedge_size=None)\n", + "for attr, group in avg_deg.items():\n", + " print(f\"Attribute '{attr}':\")\n", + " for value, mean_deg in group.items():\n", + " print(f\" {value}: {mean_deg:.2f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "6f92f126", + "metadata": {}, + "source": [ + "## 5. Temporal Consistency of Attributes\n", + "\n", + "Consistency measures how stable a node’s attribute values remain over\n", + "time (1.0 = never changes)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "ddbc777b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Node 5 consistency: {'color': 0.014524702772665599, 'role': 0.18265457785348982, 'team': 0.00884052856778128}\n", + "Node 0: {'color': 0.01452470277266571, 'role': 0.06276943678387048, 'team': 0.008840528567781392}\n", + "Node 1: {'color': 0.07678032766449228, 'role': 0.06276943678387048, 'team': 0.06276943678387048}\n", + "Node 66: {'color': 0.23903595255631893, 'role': 0.06276943678387048, 'team': 0.18265457785348982}\n" + ] + } + ], + "source": [ + "# For a single node:\n", + "consistency_node_5 = attribute_consistency(ash, node=5)\n", + "print(\"Node 5 consistency:\", consistency_node_5)\n", + "\n", + "# For all nodes:\n", + "all_consistency = attribute_consistency(ash)\n", + "# Example: show first 3 nodes\n", + "for n, cons in list(all_consistency.items())[:3]:\n", + " print(f\"Node {n}: {cons}\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.20" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/02-walks.ipynb b/tutorial/02-walks.ipynb new file mode 100644 index 0000000..ead3973 --- /dev/null +++ b/tutorial/02-walks.ipynb @@ -0,0 +1,403 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bd247875", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "Author: Andrea Failla
\n", + "Python version: 3.9
\n", + "ASH version: 0.1.0
\n", + "Last update: July 2025\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "494945cd", + "metadata": {}, + "source": [ + "# ASH Walks" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "36d1b330", + "metadata": {}, + "outputs": [], + "source": [ + "#!pip install -e ../" + ] + }, + { + "cell_type": "markdown", + "id": "b189b6f6", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "6e216381", + "metadata": {}, + "source": [ + "\n", + "## Introduction\n", + "\n", + "The ASH (Attributed Stream Hypergraph) allows to compute walks on both static and temporal hypergraphs.\n", + "\n", + "This tutorial will guide you through walk‑based algorithms provided by the library.\n" + ] + }, + { + "cell_type": "markdown", + "id": "3784a6b9", + "metadata": {}, + "source": [ + "\n", + "## Basic Concepts\n", + "\n", + "\n", + "### What is a Hypergraph walk?\n", + "A **hypergraph walk** generalises the familiar idea of a graph walk to hypergraphs by tracing a sequence of *hyperedges* rather than individual vertices.\n", + "\n", + "For a positive integer $s$, an $s$-walk of length $k$ between hyperedges $f$ and $g$ is a sequence \n", + "\n", + "$$\n", + "f = e_{i_0},\\; e_{i_1},\\; \\dots,\\; e_{i_k}=g\n", + "$$\n", + "\n", + "such that each consecutive pair overlaps in **at least $s$ vertices**, i.e. \n", + "$|e_{i_{j-1}} \\cap e_{i_j}| \\ge s$ for every $j = 1,\\dots,k$.\n", + "\n", + "Setting $s = 1$ recovers ordinary graph walks; larger $s$ values define walks that have **no counterpart in graphs** and are unique to hypergraphs.\n", + "\n", + "\n", + "[🔝 To top](#table-of-contents)\n" + ] + }, + { + "cell_type": "markdown", + "id": "a7aa57bd", + "metadata": {}, + "source": [ + "### What is a Time-respecting *s*-walk? \n", + "\n", + "In a temporal hypergraph, s-walks must also respect temporal constraints.\n", + "\n", + "A **time-respecting *s*-walk** of **length** *k*, **width** *s*, and **duration** *d* is an s-walk where the timestamps of subsquent hyperedges are non-decreasing: $t_i \\le t_{i+1}$.\n", + "\n", + "When \\(s=1\\) the notion collapses to the familiar time-respecting path on a graph; larger *s* enforce thicker overlaps and highlight genuinely higher-order, temporally feasible routes.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "0f28e683", + "metadata": {}, + "source": [ + "## Static s-walks\n", + "We start with a small handcrafted static hypergraph so results are transparent.\n", + "\n", + "We will manually add a few hyperedges so that multiple s-walks exist between pairs.\n", + "\n", + "Parameters you will often vary:\n", + "- `s`: minimum overlap size\n", + "- Source / target hyperedge IDs\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "ef186785", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hyperedges: ['e5', 'e1', 'e2', 'e3', 'e4']\n", + "e5 -> frozenset({1, 3, 5})\n", + "e1 -> frozenset({1, 2, 3})\n", + "e2 -> frozenset({2, 3, 4})\n", + "e3 -> frozenset({3, 4, 5})\n", + "e4 -> frozenset({4, 5, 6})\n" + ] + } + ], + "source": [ + "from ash_model import ASH\n", + "from ash_model.paths import shortest_s_walk, all_shortest_s_walks, all_shortest_s_walk_lengths, s_components, s_diameter\n", + "\n", + "H = ASH()\n", + "# Create deterministic hyperedges at t=0\n", + "H.add_hyperedge([1,2,3], start=0)\n", + "H.add_hyperedge([2,3,4], start=0)\n", + "H.add_hyperedge([3,4,5], start=0)\n", + "H.add_hyperedge([4,5,6], start=0)\n", + "H.add_hyperedge([1,3,5], start=0) # chord-like\n", + "\n", + "print('Hyperedges:', list(H.hyperedges()))\n", + "for hid in H.hyperedges():\n", + " print(hid, '->', H.get_hyperedge_nodes(hid))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "2e98b00b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shortest s-walk 2 from e1 to e4: ['e1', 'e5', 'e3', 'e4']\n", + "Explicit shortest: ['e1', 'e5', 'e3', 'e4']\n", + "Length summary to target: 4\n", + "Number of s-components: 1\n", + "Largest component size (edges): 5\n", + "s-diameter: 3\n" + ] + } + ], + "source": [ + "s = 2\n", + "src = 'e1'\n", + "trg = 'e4'\n", + "all_walks = all_shortest_s_walks(H, s, hyperedge_a=src)\n", + "print(f\"Shortest s-walk {s} from {src} to {trg}:\", all_walks[trg])\n", + "print('Explicit shortest:', shortest_s_walk(H, s, src, trg))\n", + "\n", + "lengths = all_shortest_s_walk_lengths(H, s, hyperedge_a=src)\n", + "print('Length summary to target:', lengths[src][trg])\n", + "\n", + "comps = list(s_components(H, s))\n", + "print('Number of s-components:', len(comps))\n", + "print('Largest component size (edges):', len(max(comps, key=len)))\n", + "print('s-diameter:', s_diameter(H, s))" + ] + }, + { + "cell_type": "markdown", + "id": "bb50713f", + "metadata": {}, + "source": [ + "## Time-respecting s-walks (example)\n", + "We now create a small temporal instance where hyperedges activate at different times.\n", + "We then enumerate time-respecting s-walks and annotate them.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "0679edc1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Attributed Stream Hypergraph\n", + "Nodes: 100\n", + "Hyperedges: 943\n", + "Snapshots: 3\n", + "Node attributes: \n", + "\n", + "One time-respecting s-walk e1 -> e4: defaultdict(, {})\n" + ] + } + ], + "source": [ + "from ash_model.paths import time_respecting_s_walks, all_time_respecting_s_walks, annotate_walks\n", + "import networkx as nx\n", + "from ash_model import ASH\n", + "from ash_model.utils import from_networkx_maximal_cliques_list\n", + "\n", + "snapshots = [nx.barabasi_albert_graph(100, 5) for _ in range(3)]\n", + "T = from_networkx_maximal_cliques_list(snapshots)\n", + "print(T)\n", + "\n", + "\n", + "s = 2\n", + "tr_walk = time_respecting_s_walks(T, s, start_from='e1', stop_at='e4')\n", + "print('One time-respecting s-walk e1 -> e4:', tr_walk)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "84812266", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "All time-respecting s-walks (s=3): {('e329', 'e367'): [[TemporalEdge(fr='e329', to='e367', weight=3, tid=1)]], ('e329', 'e330'): [[TemporalEdge(fr='e329', to='e330', weight=3, tid=1)]], ('e329', 'e394'): [[TemporalEdge(fr='e329', to='e394', weight=3, tid=1)]], ('e329', 'e331'): [[TemporalEdge(fr='e329', to='e331', weight=4, tid=1)]], ('e329', 'e326'): [[TemporalEdge(fr='e329', to='e326', weight=3, tid=1)]], ('e329', 'e332'): [[TemporalEdge(fr='e329', to='e332', weight=3, tid=1)]], ('e329', 'e333'): [[TemporalEdge(fr='e329', to='e333', weight=3, tid=1)]], ('e329', 'e379'): [[TemporalEdge(fr='e329', to='e379', weight=3, tid=1)]], ('e329', 'e325'): [[TemporalEdge(fr='e329', to='e325', weight=3, tid=1)]], ('e329', 'e551'): [[TemporalEdge(fr='e329', to='e551', weight=3, tid=1)]], ('e329', 'e327'): [[TemporalEdge(fr='e329', to='e327', weight=4, tid=1)]], ('e329', 'e480'): [[TemporalEdge(fr='e329', to='e480', weight=3, tid=1)]], ('e329', 'e328'): [[TemporalEdge(fr='e329', to='e328', weight=4, tid=1)]], ('e124', 'e125'): [[TemporalEdge(fr='e124', to='e125', weight=3, tid=0)]], ('e124', 'e13'): [[TemporalEdge(fr='e124', to='e13', weight=3, tid=0)]], ('e669', 'e678'): [[TemporalEdge(fr='e669', to='e678', weight=3, tid=2)]], ('e49', 'e17'): [[TemporalEdge(fr='e49', to='e17', weight=3, tid=0)]], ('e49', 'e36'): [[TemporalEdge(fr='e49', to='e36', weight=3, tid=0)]], ('e49', 'e24'): [[TemporalEdge(fr='e49', to='e24', weight=3, tid=0)]], ('e200', 'e154'): [[TemporalEdge(fr='e200', to='e154', weight=3, tid=0)]], ('e200', 'e35'): [[TemporalEdge(fr='e200', to='e35', weight=3, tid=0)]], ('e689', 'e691'): [[TemporalEdge(fr='e689', to='e691', weight=3, tid=2)]], ('e689', 'e690'): [[TemporalEdge(fr='e689', to='e690', weight=3, tid=2)]], ('e689', 'e672'): [[TemporalEdge(fr='e689', to='e672', weight=3, tid=2)]], ('e112', 'e110'): [[TemporalEdge(fr='e112', to='e110', weight=3, tid=0)]], ('e112', 'e30'): [[TemporalEdge(fr='e112', to='e30', weight=3, tid=0)]], ('e112', 'e143'): [[TemporalEdge(fr='e112', to='e143', weight=3, tid=0)]], ('e62', 'e11'): [[TemporalEdge(fr='e62', to='e11', weight=3, tid=0)]], ('e62', 'e23'): [[TemporalEdge(fr='e62', to='e23', weight=3, tid=0)]], ('e125', 'e124'): [[TemporalEdge(fr='e125', to='e124', weight=3, tid=0)]], ('e125', 'e10'): [[TemporalEdge(fr='e125', to='e10', weight=3, tid=0)]], ('e110', 'e112'): [[TemporalEdge(fr='e110', to='e112', weight=3, tid=0)]], ('e110', 'e222'): [[TemporalEdge(fr='e110', to='e222', weight=3, tid=0)]], ('e110', 'e9'): [[TemporalEdge(fr='e110', to='e9', weight=3, tid=0)]], ('e110', 'e4'): [[TemporalEdge(fr='e110', to='e4', weight=3, tid=0)]], ('e110', 'e74'): [[TemporalEdge(fr='e110', to='e74', weight=3, tid=0)]], ('e737', 'e736'): [[TemporalEdge(fr='e737', to='e736', weight=3, tid=2)]], ('e737', 'e833'): [[TemporalEdge(fr='e737', to='e833', weight=3, tid=2)]], ('e36', 'e49'): [[TemporalEdge(fr='e36', to='e49', weight=3, tid=0)]], ('e36', 'e37'): [[TemporalEdge(fr='e36', to='e37', weight=3, tid=0)]], ('e36', 'e24'): [[TemporalEdge(fr='e36', to='e24', weight=3, tid=0)]], ('e36', 'e35'): [[TemporalEdge(fr='e36', to='e35', weight=3, tid=0)]], ('e476', 'e330'): [[TemporalEdge(fr='e476', to='e330', weight=3, tid=1)]], ('e476', 'e331'): [[TemporalEdge(fr='e476', to='e331', weight=3, tid=1)]], ('e321', 'e330'): [[TemporalEdge(fr='e321', to='e330', weight=3, tid=1)]], ('e321', 'e333'): [[TemporalEdge(fr='e321', to='e333', weight=3, tid=1)]], ('e321', 'e320'): [[TemporalEdge(fr='e321', to='e320', weight=3, tid=1)]], ('e321', 'e328'): [[TemporalEdge(fr='e321', to='e328', weight=3, tid=1)]], ('e144', 'e142'): [[TemporalEdge(fr='e144', to='e142', weight=3, tid=0)]], ('e144', 'e314'): [[TemporalEdge(fr='e144', to='e314', weight=3, tid=0)]], ('e144', 'e9'): [[TemporalEdge(fr='e144', to='e9', weight=3, tid=0)]], ('e144', 'e143'): [[TemporalEdge(fr='e144', to='e143', weight=3, tid=0)]], ('e144', 'e170'): [[TemporalEdge(fr='e144', to='e170', weight=3, tid=0)]], ('e10', 'e125'): [[TemporalEdge(fr='e10', to='e125', weight=3, tid=0)]], ('e10', 'e15'): [[TemporalEdge(fr='e10', to='e15', weight=3, tid=0)]], ('e10', 'e14'): [[TemporalEdge(fr='e10', to='e14', weight=3, tid=0)]], ('e10', 'e12'): [[TemporalEdge(fr='e10', to='e12', weight=3, tid=0)]], ('e10', 'e9'): [[TemporalEdge(fr='e10', to='e9', weight=4, tid=0)]], ('e10', 'e292'): [[TemporalEdge(fr='e10', to='e292', weight=3, tid=0)]], ('e10', 'e4'): [[TemporalEdge(fr='e10', to='e4', weight=3, tid=0)]], ('e10', 'e13'): [[TemporalEdge(fr='e10', to='e13', weight=3, tid=0)]], ('e10', 'e3'): [[TemporalEdge(fr='e10', to='e3', weight=3, tid=0)]], ('e10', 'e11'): [[TemporalEdge(fr='e10', to='e11', weight=4, tid=0)]], ('e10', 'e23'): [[TemporalEdge(fr='e10', to='e23', weight=3, tid=0)]], ('e389', 'e380'): [[TemporalEdge(fr='e389', to='e380', weight=3, tid=1)]], ('e336', 'e367'): [[TemporalEdge(fr='e336', to='e367', weight=3, tid=1)]], ('e336', 'e337'): [[TemporalEdge(fr='e336', to='e337', weight=3, tid=1)]], ('e330', 'e329'): [[TemporalEdge(fr='e330', to='e329', weight=3, tid=1)]], ('e330', 'e476'): [[TemporalEdge(fr='e330', to='e476', weight=3, tid=1)]], ('e330', 'e321'): [[TemporalEdge(fr='e330', to='e321', weight=3, tid=1)]], ('e330', 'e331'): [[TemporalEdge(fr='e330', to='e331', weight=4, tid=1)]], ('e330', 'e326'): [[TemporalEdge(fr='e330', to='e326', weight=3, tid=1)]], ('e330', 'e332'): [[TemporalEdge(fr='e330', to='e332', weight=3, tid=1)]], ('e330', 'e333'): [[TemporalEdge(fr='e330', to='e333', weight=4, tid=1)]], ('e330', 'e325'): [[TemporalEdge(fr='e330', to='e325', weight=3, tid=1)]], ('e330', 'e327'): [[TemporalEdge(fr='e330', to='e327', weight=3, tid=1)]], ('e330', 'e328'): [[TemporalEdge(fr='e330', to='e328', weight=4, tid=1)]], ('e394', 'e329'): [[TemporalEdge(fr='e394', to='e329', weight=3, tid=1)]], ('e394', 'e395'): [[TemporalEdge(fr='e394', to='e395', weight=3, tid=1)]], ('e394', 'e397'): [[TemporalEdge(fr='e394', to='e397', weight=3, tid=1)]], ('e394', 'e385'): [[TemporalEdge(fr='e394', to='e385', weight=3, tid=1)]], ('e394', 'e551'): [[TemporalEdge(fr='e394', to='e551', weight=3, tid=1)]], ('e471', 'e498'): [[TemporalEdge(fr='e471', to='e498', weight=3, tid=1)]], ('e222', 'e110'): [[TemporalEdge(fr='e222', to='e110', weight=3, tid=0)]], ('e222', 'e9'): [[TemporalEdge(fr='e222', to='e9', weight=3, tid=0)]], ('e222', 'e4'): [[TemporalEdge(fr='e222', to='e4', weight=3, tid=0)]], ('e628', 'e673'): [[TemporalEdge(fr='e628', to='e673', weight=3, tid=2)]], ('e628', 'e325'): [[TemporalEdge(fr='e628', to='e325', weight=3, tid=2)]], ('e628', 'e644'): [[TemporalEdge(fr='e628', to='e644', weight=3, tid=2)]], ('e628', 'e820'): [[TemporalEdge(fr='e628', to='e820', weight=3, tid=2)]], ('e628', 'e652'): [[TemporalEdge(fr='e628', to='e652', weight=3, tid=2)]], ('e637', 'e325'): [[TemporalEdge(fr='e637', to='e325', weight=3, tid=2)]], ('e16', 'e17'): [[TemporalEdge(fr='e16', to='e17', weight=3, tid=0)]], ('e16', 'e9'): [[TemporalEdge(fr='e16', to='e9', weight=3, tid=0)]], ('e16', 'e18'): [[TemporalEdge(fr='e16', to='e18', weight=3, tid=0)]], ('e19', 'e12'): [[TemporalEdge(fr='e19', to='e12', weight=3, tid=0)]], ('e19', 'e20'): [[TemporalEdge(fr='e19', to='e20', weight=3, tid=0)]], ('e382', 'e381'): [[TemporalEdge(fr='e382', to='e381', weight=3, tid=1)]], ('e382', 'e380'): [[TemporalEdge(fr='e382', to='e380', weight=3, tid=1)]], ('e736', 'e737'): [[TemporalEdge(fr='e736', to='e737', weight=3, tid=2)]], ('e736', 'e643'): [[TemporalEdge(fr='e736', to='e643', weight=3, tid=2)]], ('e515', 'e327'): [[TemporalEdge(fr='e515', to='e327', weight=3, tid=1)]], ('e333', 'e329'): [[TemporalEdge(fr='e333', to='e329', weight=3, tid=1)]], ('e333', 'e321'): [[TemporalEdge(fr='e333', to='e321', weight=3, tid=1)]], ('e333', 'e330'): [[TemporalEdge(fr='e333', to='e330', weight=4, tid=1)]], ('e333', 'e331'): [[TemporalEdge(fr='e333', to='e331', weight=3, tid=1)]], ('e333', 'e326'): [[TemporalEdge(fr='e333', to='e326', weight=3, tid=1)]], ('e333', 'e332'): [[TemporalEdge(fr='e333', to='e332', weight=4, tid=1)]], ('e333', 'e325'): [[TemporalEdge(fr='e333', to='e325', weight=3, tid=1)]], ('e333', 'e327'): [[TemporalEdge(fr='e333', to='e327', weight=3, tid=1)]], ('e333', 'e328'): [[TemporalEdge(fr='e333', to='e328', weight=4, tid=1)]], ('e645', 'e646'): [[TemporalEdge(fr='e645', to='e646', weight=3, tid=2)]], ('e645', 'e630'): [[TemporalEdge(fr='e645', to='e630', weight=3, tid=2)]], ('e385', 'e397'): [[TemporalEdge(fr='e385', to='e397', weight=3, tid=1)]], ('e385', 'e394'): [[TemporalEdge(fr='e385', to='e394', weight=3, tid=1)]], ('e385', 'e379'): [[TemporalEdge(fr='e385', to='e379', weight=3, tid=1)]], ('e690', 'e689'): [[TemporalEdge(fr='e690', to='e689', weight=3, tid=2)]], ('e690', 'e691'): [[TemporalEdge(fr='e690', to='e691', weight=3, tid=2)]], ('e37', 'e36'): [[TemporalEdge(fr='e37', to='e36', weight=3, tid=0)]], ('e37', 'e21'): [[TemporalEdge(fr='e37', to='e21', weight=3, tid=0)]], ('e37', 'e35'): [[TemporalEdge(fr='e37', to='e35', weight=3, tid=0)]], ('e379', 'e329'): [[TemporalEdge(fr='e379', to='e329', weight=3, tid=1)]], ('e379', 'e385'): [[TemporalEdge(fr='e379', to='e385', weight=3, tid=1)]], ('e379', 'e380'): [[TemporalEdge(fr='e379', to='e380', weight=3, tid=1)]], ('e12', 'e10'): [[TemporalEdge(fr='e12', to='e10', weight=3, tid=0)]], ('e12', 'e19'): [[TemporalEdge(fr='e12', to='e19', weight=3, tid=0)]], ('e12', 'e14'): [[TemporalEdge(fr='e12', to='e14', weight=3, tid=0)]], ('e12', 'e9'): [[TemporalEdge(fr='e12', to='e9', weight=3, tid=0)]], ('e12', 'e13'): [[TemporalEdge(fr='e12', to='e13', weight=3, tid=0)]], ('e12', 'e11'): [[TemporalEdge(fr='e12', to='e11', weight=3, tid=0)]], ('e9', 'e110'): [[TemporalEdge(fr='e9', to='e110', weight=3, tid=0)]], ('e9', 'e15'): [[TemporalEdge(fr='e9', to='e15', weight=3, tid=0)]], ('e9', 'e144'): [[TemporalEdge(fr='e9', to='e144', weight=3, tid=0)]], ('e9', 'e10'): [[TemporalEdge(fr='e9', to='e10', weight=4, tid=0)]], ('e9', 'e222'): [[TemporalEdge(fr='e9', to='e222', weight=3, tid=0)]], ('e9', 'e16'): [[TemporalEdge(fr='e9', to='e16', weight=3, tid=0)]], ('e9', 'e14'): [[TemporalEdge(fr='e9', to='e14', weight=3, tid=0)]], ('e9', 'e314'): [[TemporalEdge(fr='e9', to='e314', weight=3, tid=0)]], ('e9', 'e30'): [[TemporalEdge(fr='e9', to='e30', weight=3, tid=0)]], ('e9', 'e12'): [[TemporalEdge(fr='e9', to='e12', weight=3, tid=0)]], ('e9', 'e292'): [[TemporalEdge(fr='e9', to='e292', weight=3, tid=0)]], ('e9', 'e4'): [[TemporalEdge(fr='e9', to='e4', weight=4, tid=0)]], ('e9', 'e13'): [[TemporalEdge(fr='e9', to='e13', weight=3, tid=0)]], ('e9', 'e3'): [[TemporalEdge(fr='e9', to='e3', weight=3, tid=0)]], ('e9', 'e11'): [[TemporalEdge(fr='e9', to='e11', weight=4, tid=0)]], ('e9', 'e18'): [[TemporalEdge(fr='e9', to='e18', weight=3, tid=0)]], ('e9', 'e170'): [[TemporalEdge(fr='e9', to='e170', weight=3, tid=0)]], ('e9', 'e23'): [[TemporalEdge(fr='e9', to='e23', weight=3, tid=0)]], ('e325', 'e329'): [[TemporalEdge(fr='e325', to='e329', weight=3, tid=1)]], ('e325', 'e330'): [[TemporalEdge(fr='e325', to='e330', weight=3, tid=1)]], ('e325', 'e331'): [[TemporalEdge(fr='e325', to='e331', weight=3, tid=1)]], ('e325', 'e326'): [[TemporalEdge(fr='e325', to='e326', weight=3, tid=1)]], ('e325', 'e332'): [[TemporalEdge(fr='e325', to='e332', weight=3, tid=1)]], ('e325', 'e333'): [[TemporalEdge(fr='e325', to='e333', weight=3, tid=1)]], ('e325', 'e327'): [[TemporalEdge(fr='e325', to='e327', weight=3, tid=1)]], ('e325', 'e328'): [[TemporalEdge(fr='e325', to='e328', weight=3, tid=1)]], ('e325', 'e628'): [[TemporalEdge(fr='e325', to='e628', weight=3, tid=2)]], ('e325', 'e637'): [[TemporalEdge(fr='e325', to='e637', weight=3, tid=2)]], ('e325', 'e644'): [[TemporalEdge(fr='e325', to='e644', weight=3, tid=2)]], ('e544', 'e367'): [[TemporalEdge(fr='e544', to='e367', weight=3, tid=1)]], ('e544', 'e327'): [[TemporalEdge(fr='e544', to='e327', weight=3, tid=1)]], ('e544', 'e545'): [[TemporalEdge(fr='e544', to='e545', weight=3, tid=1)]], ('e320', 'e321'): [[TemporalEdge(fr='e320', to='e321', weight=3, tid=1)]], ('e320', 'e332'): [[TemporalEdge(fr='e320', to='e332', weight=3, tid=1)]], ('e320', 'e327'): [[TemporalEdge(fr='e320', to='e327', weight=3, tid=1)]], ('e292', 'e10'): [[TemporalEdge(fr='e292', to='e10', weight=3, tid=0)]], ('e292', 'e9'): [[TemporalEdge(fr='e292', to='e9', weight=3, tid=0)]], ('e292', 'e11'): [[TemporalEdge(fr='e292', to='e11', weight=3, tid=0)]], ('e2', 'e3'): [[TemporalEdge(fr='e2', to='e3', weight=3, tid=0)]], ('e425', 'e424'): [[TemporalEdge(fr='e425', to='e424', weight=3, tid=1)]], ('e425', 'e328'): [[TemporalEdge(fr='e425', to='e328', weight=3, tid=1)]], ('e687', 'e691'): [[TemporalEdge(fr='e687', to='e691', weight=3, tid=2)]], ('e414', 'e413'): [[TemporalEdge(fr='e414', to='e413', weight=3, tid=1)]], ('e21', 'e17'): [[TemporalEdge(fr='e21', to='e17', weight=3, tid=0)]], ('e21', 'e15'): [[TemporalEdge(fr='e21', to='e15', weight=3, tid=0)]], ('e21', 'e37'): [[TemporalEdge(fr='e21', to='e37', weight=3, tid=0)]], ('e21', 'e11'): [[TemporalEdge(fr='e21', to='e11', weight=3, tid=0)]], ('e334', 'e335'): [[TemporalEdge(fr='e334', to='e335', weight=3, tid=1)]], ('e545', 'e544'): [[TemporalEdge(fr='e545', to='e544', weight=3, tid=1)]], ('e545', 'e328'): [[TemporalEdge(fr='e545', to='e328', weight=3, tid=1)]], ('e74', 'e110'): [[TemporalEdge(fr='e74', to='e110', weight=3, tid=0)]], ('e74', 'e75'): [[TemporalEdge(fr='e74', to='e75', weight=3, tid=0)]], ('e154', 'e200'): [[TemporalEdge(fr='e154', to='e200', weight=3, tid=0)]], ('e154', 'e153'): [[TemporalEdge(fr='e154', to='e153', weight=3, tid=0)]], ('e154', 'e35'): [[TemporalEdge(fr='e154', to='e35', weight=3, tid=0)]], ('e820', 'e628'): [[TemporalEdge(fr='e820', to='e628', weight=3, tid=2)]], ('e672', 'e689'): [[TemporalEdge(fr='e672', to='e689', weight=3, tid=2)]], ('e672', 'e671'): [[TemporalEdge(fr='e672', to='e671', weight=3, tid=2)]], ('e672', 'e673'): [[TemporalEdge(fr='e672', to='e673', weight=3, tid=2)]], ('e25', 'e15'): [[TemporalEdge(fr='e25', to='e15', weight=3, tid=0)]], ('e25', 'e27'): [[TemporalEdge(fr='e25', to='e27', weight=3, tid=0)]], ('e25', 'e30'): [[TemporalEdge(fr='e25', to='e30', weight=3, tid=0)]], ('e25', 'e22'): [[TemporalEdge(fr='e25', to='e22', weight=4, tid=0)]], ('e25', 'e3'): [[TemporalEdge(fr='e25', to='e3', weight=3, tid=0)]], ('e25', 'e23'): [[TemporalEdge(fr='e25', to='e23', weight=3, tid=0)]], ('e643', 'e646'): [[TemporalEdge(fr='e643', to='e646', weight=3, tid=2)]], ('e643', 'e736'): [[TemporalEdge(fr='e643', to='e736', weight=3, tid=2)]], ('e643', 'e644'): [[TemporalEdge(fr='e643', to='e644', weight=3, tid=2)]], ('e413', 'e414'): [[TemporalEdge(fr='e413', to='e414', weight=3, tid=1)]], ('e143', 'e112'): [[TemporalEdge(fr='e143', to='e112', weight=3, tid=0)]], ('e143', 'e142'): [[TemporalEdge(fr='e143', to='e142', weight=3, tid=0)]], ('e143', 'e144'): [[TemporalEdge(fr='e143', to='e144', weight=3, tid=0)]], ('e143', 'e30'): [[TemporalEdge(fr='e143', to='e30', weight=3, tid=0)]], ('e143', 'e148'): [[TemporalEdge(fr='e143', to='e148', weight=3, tid=0)]], ('e153', 'e15'): [[TemporalEdge(fr='e153', to='e15', weight=3, tid=0)]], ('e153', 'e22'): [[TemporalEdge(fr='e153', to='e22', weight=3, tid=0)]], ('e153', 'e154'): [[TemporalEdge(fr='e153', to='e154', weight=3, tid=0)]], ('e35', 'e200'): [[TemporalEdge(fr='e35', to='e200', weight=3, tid=0)]], ('e35', 'e15'): [[TemporalEdge(fr='e35', to='e15', weight=3, tid=0)]], ('e35', 'e36'): [[TemporalEdge(fr='e35', to='e36', weight=3, tid=0)]], ('e35', 'e37'): [[TemporalEdge(fr='e35', to='e37', weight=3, tid=0)]], ('e35', 'e22'): [[TemporalEdge(fr='e35', to='e22', weight=3, tid=0)]], ('e35', 'e154'): [[TemporalEdge(fr='e35', to='e154', weight=3, tid=0)]], ('e11', 'e17'): [[TemporalEdge(fr='e11', to='e17', weight=3, tid=0)]], ('e11', 'e62'): [[TemporalEdge(fr='e11', to='e62', weight=3, tid=0)]], ('e11', 'e15'): [[TemporalEdge(fr='e11', to='e15', weight=4, tid=0)]], ('e11', 'e10'): [[TemporalEdge(fr='e11', to='e10', weight=4, tid=0)]], ('e11', 'e14'): [[TemporalEdge(fr='e11', to='e14', weight=3, tid=0)]], ('e11', 'e12'): [[TemporalEdge(fr='e11', to='e12', weight=3, tid=0)]], ('e11', 'e9'): [[TemporalEdge(fr='e11', to='e9', weight=4, tid=0)]], ('e11', 'e292'): [[TemporalEdge(fr='e11', to='e292', weight=3, tid=0)]], ('e11', 'e22'): [[TemporalEdge(fr='e11', to='e22', weight=3, tid=0)]], ('e11', 'e4'): [[TemporalEdge(fr='e11', to='e4', weight=3, tid=0)]], ('e11', 'e21'): [[TemporalEdge(fr='e11', to='e21', weight=3, tid=0)]], ('e11', 'e13'): [[TemporalEdge(fr='e11', to='e13', weight=3, tid=0)]], ('e11', 'e3'): [[TemporalEdge(fr='e11', to='e3', weight=3, tid=0)]], ('e11', 'e23'): [[TemporalEdge(fr='e11', to='e23', weight=4, tid=0)]], ('e18', 'e16'): [[TemporalEdge(fr='e18', to='e16', weight=3, tid=0)]], ('e18', 'e5'): [[TemporalEdge(fr='e18', to='e5', weight=3, tid=0)]], ('e18', 'e9'): [[TemporalEdge(fr='e18', to='e9', weight=3, tid=0)]], ('e18', 'e38'): [[TemporalEdge(fr='e18', to='e38', weight=3, tid=0)]], ('e170', 'e171'): [[TemporalEdge(fr='e170', to='e171', weight=3, tid=0)]], ('e170', 'e144'): [[TemporalEdge(fr='e170', to='e144', weight=3, tid=0)]], ('e170', 'e314'): [[TemporalEdge(fr='e170', to='e314', weight=3, tid=0)]], ('e170', 'e9'): [[TemporalEdge(fr='e170', to='e9', weight=3, tid=0)]], ('e23', 'e62'): [[TemporalEdge(fr='e23', to='e62', weight=3, tid=0)]], ('e23', 'e15'): [[TemporalEdge(fr='e23', to='e15', weight=3, tid=0)]], ('e23', 'e10'): [[TemporalEdge(fr='e23', to='e10', weight=3, tid=0)]], ('e23', 'e9'): [[TemporalEdge(fr='e23', to='e9', weight=3, tid=0)]], ('e23', 'e22'): [[TemporalEdge(fr='e23', to='e22', weight=4, tid=0)]], ('e23', 'e4'): [[TemporalEdge(fr='e23', to='e4', weight=3, tid=0)]], ('e23', 'e24'): [[TemporalEdge(fr='e23', to='e24', weight=3, tid=0)]], ('e23', 'e25'): [[TemporalEdge(fr='e23', to='e25', weight=3, tid=0)]], ('e23', 'e3'): [[TemporalEdge(fr='e23', to='e3', weight=4, tid=0)]], ('e23', 'e11'): [[TemporalEdge(fr='e23', to='e11', weight=4, tid=0)]], ('e17', 'e49'): [[TemporalEdge(fr='e17', to='e49', weight=3, tid=0)]], ('e17', 'e15'): [[TemporalEdge(fr='e17', to='e15', weight=3, tid=0)]], ('e17', 'e16'): [[TemporalEdge(fr='e17', to='e16', weight=3, tid=0)]], ('e17', 'e21'): [[TemporalEdge(fr='e17', to='e21', weight=3, tid=0)]], ('e17', 'e11'): [[TemporalEdge(fr='e17', to='e11', weight=3, tid=0)]], ('e646', 'e645'): [[TemporalEdge(fr='e646', to='e645', weight=3, tid=2)]], ('e646', 'e643'): [[TemporalEdge(fr='e646', to='e643', weight=3, tid=2)]], ('e646', 'e833'): [[TemporalEdge(fr='e646', to='e833', weight=3, tid=2)]], ('e367', 'e329'): [[TemporalEdge(fr='e367', to='e329', weight=3, tid=1)]], ('e367', 'e336'): [[TemporalEdge(fr='e367', to='e336', weight=3, tid=1)]], ('e367', 'e544'): [[TemporalEdge(fr='e367', to='e544', weight=3, tid=1)]], ('e367', 'e327'): [[TemporalEdge(fr='e367', to='e327', weight=4, tid=1)]], ('e367', 'e328'): [[TemporalEdge(fr='e367', to='e328', weight=3, tid=1)]], ('e142', 'e144'): [[TemporalEdge(fr='e142', to='e144', weight=3, tid=0)]], ('e142', 'e143'): [[TemporalEdge(fr='e142', to='e143', weight=3, tid=0)]], ('e670', 'e671'): [[TemporalEdge(fr='e670', to='e671', weight=3, tid=2)]], ('e670', 'e630'): [[TemporalEdge(fr='e670', to='e630', weight=3, tid=2)]], ('e670', 'e679'): [[TemporalEdge(fr='e670', to='e679', weight=3, tid=2)]], ('e498', 'e337'): [[TemporalEdge(fr='e498', to='e337', weight=3, tid=1)]], ('e498', 'e471'): [[TemporalEdge(fr='e498', to='e471', weight=3, tid=1)]], ('e395', 'e394'): [[TemporalEdge(fr='e395', to='e394', weight=3, tid=1)]], ('e395', 'e480'): [[TemporalEdge(fr='e395', to='e480', weight=3, tid=1)]], ('e368', 'e327'): [[TemporalEdge(fr='e368', to='e327', weight=3, tid=1)]], ('e397', 'e394'): [[TemporalEdge(fr='e397', to='e394', weight=3, tid=1)]], ('e397', 'e385'): [[TemporalEdge(fr='e397', to='e385', weight=3, tid=1)]], ('e15', 'e17'): [[TemporalEdge(fr='e15', to='e17', weight=3, tid=0)]], ('e15', 'e171'): [[TemporalEdge(fr='e15', to='e171', weight=3, tid=0)]], ('e15', 'e10'): [[TemporalEdge(fr='e15', to='e10', weight=3, tid=0)]], ('e15', 'e9'): [[TemporalEdge(fr='e15', to='e9', weight=3, tid=0)]], ('e15', 'e22'): [[TemporalEdge(fr='e15', to='e22', weight=4, tid=0)]], ('e15', 'e21'): [[TemporalEdge(fr='e15', to='e21', weight=3, tid=0)]], ('e15', 'e25'): [[TemporalEdge(fr='e15', to='e25', weight=3, tid=0)]], ('e15', 'e153'): [[TemporalEdge(fr='e15', to='e153', weight=3, tid=0)]], ('e15', 'e35'): [[TemporalEdge(fr='e15', to='e35', weight=3, tid=0)]], ('e15', 'e11'): [[TemporalEdge(fr='e15', to='e11', weight=4, tid=0)]], ('e15', 'e23'): [[TemporalEdge(fr='e15', to='e23', weight=3, tid=0)]], ('e129', 'e27'): [[TemporalEdge(fr='e129', to='e27', weight=3, tid=0)]], ('e27', 'e129'): [[TemporalEdge(fr='e27', to='e129', weight=3, tid=0)]], ('e27', 'e22'): [[TemporalEdge(fr='e27', to='e22', weight=3, tid=0)]], ('e27', 'e25'): [[TemporalEdge(fr='e27', to='e25', weight=3, tid=0)]], ('e691', 'e689'): [[TemporalEdge(fr='e691', to='e689', weight=3, tid=2)]], ('e691', 'e690'): [[TemporalEdge(fr='e691', to='e690', weight=3, tid=2)]], ('e691', 'e687'): [[TemporalEdge(fr='e691', to='e687', weight=3, tid=2)]], ('e171', 'e15'): [[TemporalEdge(fr='e171', to='e15', weight=3, tid=0)]], ('e171', 'e170'): [[TemporalEdge(fr='e171', to='e170', weight=3, tid=0)]], ('e337', 'e498'): [[TemporalEdge(fr='e337', to='e498', weight=3, tid=1)]], ('e337', 'e336'): [[TemporalEdge(fr='e337', to='e336', weight=3, tid=1)]], ('e671', 'e670'): [[TemporalEdge(fr='e671', to='e670', weight=3, tid=2)]], ('e671', 'e672'): [[TemporalEdge(fr='e671', to='e672', weight=3, tid=2)]], ('e8', 'e14'): [[TemporalEdge(fr='e8', to='e14', weight=3, tid=0)]], ('e673', 'e628'): [[TemporalEdge(fr='e673', to='e628', weight=3, tid=2)]], ('e673', 'e672'): [[TemporalEdge(fr='e673', to='e672', weight=3, tid=2)]], ('e630', 'e670'): [[TemporalEdge(fr='e630', to='e670', weight=3, tid=2)]], ('e630', 'e645'): [[TemporalEdge(fr='e630', to='e645', weight=3, tid=2)]], ('e335', 'e334'): [[TemporalEdge(fr='e335', to='e334', weight=3, tid=1)]], ('e331', 'e329'): [[TemporalEdge(fr='e331', to='e329', weight=4, tid=1)]], ('e331', 'e476'): [[TemporalEdge(fr='e331', to='e476', weight=3, tid=1)]], ('e331', 'e330'): [[TemporalEdge(fr='e331', to='e330', weight=4, tid=1)]], ('e331', 'e326'): [[TemporalEdge(fr='e331', to='e326', weight=3, tid=1)]], ('e331', 'e332'): [[TemporalEdge(fr='e331', to='e332', weight=3, tid=1)]], ('e331', 'e333'): [[TemporalEdge(fr='e331', to='e333', weight=3, tid=1)]], ('e331', 'e325'): [[TemporalEdge(fr='e331', to='e325', weight=3, tid=1)]], ('e331', 'e327'): [[TemporalEdge(fr='e331', to='e327', weight=3, tid=1)]], ('e331', 'e480'): [[TemporalEdge(fr='e331', to='e480', weight=3, tid=1)]], ('e331', 'e380'): [[TemporalEdge(fr='e331', to='e380', weight=3, tid=1)]], ('e331', 'e328'): [[TemporalEdge(fr='e331', to='e328', weight=3, tid=1)]], ('e326', 'e329'): [[TemporalEdge(fr='e326', to='e329', weight=3, tid=1)]], ('e326', 'e330'): [[TemporalEdge(fr='e326', to='e330', weight=3, tid=1)]], ('e326', 'e331'): [[TemporalEdge(fr='e326', to='e331', weight=3, tid=1)]], ('e326', 'e332'): [[TemporalEdge(fr='e326', to='e332', weight=3, tid=1)]], ('e326', 'e333'): [[TemporalEdge(fr='e326', to='e333', weight=3, tid=1)]], ('e326', 'e325'): [[TemporalEdge(fr='e326', to='e325', weight=3, tid=1)]], ('e326', 'e327'): [[TemporalEdge(fr='e326', to='e327', weight=3, tid=1)]], ('e326', 'e328'): [[TemporalEdge(fr='e326', to='e328', weight=3, tid=1)]], ('e332', 'e329'): [[TemporalEdge(fr='e332', to='e329', weight=3, tid=1)]], ('e332', 'e330'): [[TemporalEdge(fr='e332', to='e330', weight=3, tid=1)]], ('e332', 'e331'): [[TemporalEdge(fr='e332', to='e331', weight=3, tid=1)]], ('e332', 'e326'): [[TemporalEdge(fr='e332', to='e326', weight=3, tid=1)]], ('e332', 'e333'): [[TemporalEdge(fr='e332', to='e333', weight=4, tid=1)]], ('e332', 'e325'): [[TemporalEdge(fr='e332', to='e325', weight=3, tid=1)]], ('e332', 'e320'): [[TemporalEdge(fr='e332', to='e320', weight=3, tid=1)]], ('e332', 'e322'): [[TemporalEdge(fr='e332', to='e322', weight=3, tid=1)]], ('e332', 'e324'): [[TemporalEdge(fr='e332', to='e324', weight=3, tid=1)]], ('e332', 'e327'): [[TemporalEdge(fr='e332', to='e327', weight=4, tid=1)]], ('e332', 'e328'): [[TemporalEdge(fr='e332', to='e328', weight=3, tid=1)]], ('e14', 'e10'): [[TemporalEdge(fr='e14', to='e10', weight=3, tid=0)]], ('e14', 'e8'): [[TemporalEdge(fr='e14', to='e8', weight=3, tid=0)]], ('e14', 'e12'): [[TemporalEdge(fr='e14', to='e12', weight=3, tid=0)]], ('e14', 'e9'): [[TemporalEdge(fr='e14', to='e9', weight=3, tid=0)]], ('e14', 'e13'): [[TemporalEdge(fr='e14', to='e13', weight=3, tid=0)]], ('e14', 'e11'): [[TemporalEdge(fr='e14', to='e11', weight=3, tid=0)]], ('e314', 'e144'): [[TemporalEdge(fr='e314', to='e144', weight=3, tid=0)]], ('e314', 'e9'): [[TemporalEdge(fr='e314', to='e9', weight=3, tid=0)]], ('e314', 'e170'): [[TemporalEdge(fr='e314', to='e170', weight=3, tid=0)]], ('e30', 'e112'): [[TemporalEdge(fr='e30', to='e112', weight=3, tid=0)]], ('e30', 'e9'): [[TemporalEdge(fr='e30', to='e9', weight=3, tid=0)]], ('e30', 'e4'): [[TemporalEdge(fr='e30', to='e4', weight=3, tid=0)]], ('e30', 'e25'): [[TemporalEdge(fr='e30', to='e25', weight=3, tid=0)]], ('e30', 'e143'): [[TemporalEdge(fr='e30', to='e143', weight=3, tid=0)]], ('e463', 'e464'): [[TemporalEdge(fr='e463', to='e464', weight=3, tid=1)]], ('e5', 'e38'): [[TemporalEdge(fr='e5', to='e38', weight=3, tid=0)]], ('e5', 'e4'): [[TemporalEdge(fr='e5', to='e4', weight=3, tid=0)]], ('e5', 'e18'): [[TemporalEdge(fr='e5', to='e18', weight=3, tid=0)]], ('e322', 'e332'): [[TemporalEdge(fr='e322', to='e332', weight=3, tid=1)]], ('e322', 'e324'): [[TemporalEdge(fr='e322', to='e324', weight=3, tid=1)]], ('e322', 'e327'): [[TemporalEdge(fr='e322', to='e327', weight=3, tid=1)]], ('e75', 'e4'): [[TemporalEdge(fr='e75', to='e4', weight=3, tid=0)]], ('e75', 'e74'): [[TemporalEdge(fr='e75', to='e74', weight=3, tid=0)]], ('e551', 'e329'): [[TemporalEdge(fr='e551', to='e329', weight=3, tid=1)]], ('e551', 'e394'): [[TemporalEdge(fr='e551', to='e394', weight=3, tid=1)]], ('e424', 'e425'): [[TemporalEdge(fr='e424', to='e425', weight=3, tid=1)]], ('e424', 'e327'): [[TemporalEdge(fr='e424', to='e327', weight=3, tid=1)]], ('e324', 'e332'): [[TemporalEdge(fr='e324', to='e332', weight=3, tid=1)]], ('e324', 'e322'): [[TemporalEdge(fr='e324', to='e322', weight=3, tid=1)]], ('e324', 'e327'): [[TemporalEdge(fr='e324', to='e327', weight=3, tid=1)]], ('e22', 'e15'): [[TemporalEdge(fr='e22', to='e15', weight=4, tid=0)]], ('e22', 'e27'): [[TemporalEdge(fr='e22', to='e27', weight=3, tid=0)]], ('e22', 'e24'): [[TemporalEdge(fr='e22', to='e24', weight=3, tid=0)]], ('e22', 'e25'): [[TemporalEdge(fr='e22', to='e25', weight=4, tid=0)]], ('e22', 'e3'): [[TemporalEdge(fr='e22', to='e3', weight=3, tid=0)]], ('e22', 'e153'): [[TemporalEdge(fr='e22', to='e153', weight=3, tid=0)]], ('e22', 'e35'): [[TemporalEdge(fr='e22', to='e35', weight=3, tid=0)]], ('e22', 'e11'): [[TemporalEdge(fr='e22', to='e11', weight=3, tid=0)]], ('e22', 'e23'): [[TemporalEdge(fr='e22', to='e23', weight=4, tid=0)]], ('e38', 'e5'): [[TemporalEdge(fr='e38', to='e5', weight=3, tid=0)]], ('e38', 'e18'): [[TemporalEdge(fr='e38', to='e18', weight=3, tid=0)]], ('e679', 'e670'): [[TemporalEdge(fr='e679', to='e670', weight=3, tid=2)]], ('e4', 'e110'): [[TemporalEdge(fr='e4', to='e110', weight=3, tid=0)]], ('e4', 'e10'): [[TemporalEdge(fr='e4', to='e10', weight=3, tid=0)]], ('e4', 'e222'): [[TemporalEdge(fr='e4', to='e222', weight=3, tid=0)]], ('e4', 'e30'): [[TemporalEdge(fr='e4', to='e30', weight=3, tid=0)]], ('e4', 'e5'): [[TemporalEdge(fr='e4', to='e5', weight=3, tid=0)]], ('e4', 'e9'): [[TemporalEdge(fr='e4', to='e9', weight=4, tid=0)]], ('e4', 'e75'): [[TemporalEdge(fr='e4', to='e75', weight=3, tid=0)]], ('e4', 'e163'): [[TemporalEdge(fr='e4', to='e163', weight=3, tid=0)]], ('e4', 'e3'): [[TemporalEdge(fr='e4', to='e3', weight=4, tid=0)]], ('e4', 'e11'): [[TemporalEdge(fr='e4', to='e11', weight=3, tid=0)]], ('e4', 'e23'): [[TemporalEdge(fr='e4', to='e23', weight=3, tid=0)]], ('e163', 'e4'): [[TemporalEdge(fr='e163', to='e4', weight=3, tid=0)]], ('e163', 'e3'): [[TemporalEdge(fr='e163', to='e3', weight=3, tid=0)]], ('e327', 'e329'): [[TemporalEdge(fr='e327', to='e329', weight=4, tid=1)]], ('e327', 'e367'): [[TemporalEdge(fr='e327', to='e367', weight=4, tid=1)]], ('e327', 'e368'): [[TemporalEdge(fr='e327', to='e368', weight=3, tid=1)]], ('e327', 'e330'): [[TemporalEdge(fr='e327', to='e330', weight=3, tid=1)]], ('e327', 'e331'): [[TemporalEdge(fr='e327', to='e331', weight=3, tid=1)]], ('e327', 'e326'): [[TemporalEdge(fr='e327', to='e326', weight=3, tid=1)]], ('e327', 'e332'): [[TemporalEdge(fr='e327', to='e332', weight=4, tid=1)]], ('e327', 'e515'): [[TemporalEdge(fr='e327', to='e515', weight=3, tid=1)]], ('e327', 'e333'): [[TemporalEdge(fr='e327', to='e333', weight=3, tid=1)]], ('e327', 'e325'): [[TemporalEdge(fr='e327', to='e325', weight=3, tid=1)]], ('e327', 'e544'): [[TemporalEdge(fr='e327', to='e544', weight=3, tid=1)]], ('e327', 'e320'): [[TemporalEdge(fr='e327', to='e320', weight=3, tid=1)]], ('e327', 'e322'): [[TemporalEdge(fr='e327', to='e322', weight=3, tid=1)]], ('e327', 'e424'): [[TemporalEdge(fr='e327', to='e424', weight=3, tid=1)]], ('e327', 'e324'): [[TemporalEdge(fr='e327', to='e324', weight=3, tid=1)]], ('e327', 'e328'): [[TemporalEdge(fr='e327', to='e328', weight=4, tid=1)]], ('e480', 'e329'): [[TemporalEdge(fr='e480', to='e329', weight=3, tid=1)]], ('e480', 'e395'): [[TemporalEdge(fr='e480', to='e395', weight=3, tid=1)]], ('e480', 'e331'): [[TemporalEdge(fr='e480', to='e331', weight=3, tid=1)]], ('e13', 'e124'): [[TemporalEdge(fr='e13', to='e124', weight=3, tid=0)]], ('e13', 'e10'): [[TemporalEdge(fr='e13', to='e10', weight=3, tid=0)]], ('e13', 'e14'): [[TemporalEdge(fr='e13', to='e14', weight=3, tid=0)]], ('e13', 'e12'): [[TemporalEdge(fr='e13', to='e12', weight=3, tid=0)]], ('e13', 'e9'): [[TemporalEdge(fr='e13', to='e9', weight=3, tid=0)]], ('e13', 'e11'): [[TemporalEdge(fr='e13', to='e11', weight=3, tid=0)]], ('e20', 'e19'): [[TemporalEdge(fr='e20', to='e19', weight=3, tid=0)]], ('e644', 'e628'): [[TemporalEdge(fr='e644', to='e628', weight=3, tid=2)]], ('e644', 'e325'): [[TemporalEdge(fr='e644', to='e325', weight=3, tid=2)]], ('e644', 'e643'): [[TemporalEdge(fr='e644', to='e643', weight=3, tid=2)]], ('e24', 'e49'): [[TemporalEdge(fr='e24', to='e49', weight=3, tid=0)]], ('e24', 'e36'): [[TemporalEdge(fr='e24', to='e36', weight=3, tid=0)]], ('e24', 'e22'): [[TemporalEdge(fr='e24', to='e22', weight=3, tid=0)]], ('e24', 'e23'): [[TemporalEdge(fr='e24', to='e23', weight=3, tid=0)]], ('e403', 'e339'): [[TemporalEdge(fr='e403', to='e339', weight=3, tid=1)]], ('e381', 'e382'): [[TemporalEdge(fr='e381', to='e382', weight=3, tid=1)]], ('e381', 'e380'): [[TemporalEdge(fr='e381', to='e380', weight=3, tid=1)]], ('e381', 'e377'): [[TemporalEdge(fr='e381', to='e377', weight=3, tid=1)]], ('e380', 'e389'): [[TemporalEdge(fr='e380', to='e389', weight=3, tid=1)]], ('e380', 'e382'): [[TemporalEdge(fr='e380', to='e382', weight=3, tid=1)]], ('e380', 'e331'): [[TemporalEdge(fr='e380', to='e331', weight=3, tid=1)]], ('e380', 'e379'): [[TemporalEdge(fr='e380', to='e379', weight=3, tid=1)]], ('e380', 'e381'): [[TemporalEdge(fr='e380', to='e381', weight=3, tid=1)]], ('e3', 'e10'): [[TemporalEdge(fr='e3', to='e10', weight=3, tid=0)]], ('e3', 'e9'): [[TemporalEdge(fr='e3', to='e9', weight=3, tid=0)]], ('e3', 'e2'): [[TemporalEdge(fr='e3', to='e2', weight=3, tid=0)]], ('e3', 'e22'): [[TemporalEdge(fr='e3', to='e22', weight=3, tid=0)]], ('e3', 'e4'): [[TemporalEdge(fr='e3', to='e4', weight=4, tid=0)]], ('e3', 'e163'): [[TemporalEdge(fr='e3', to='e163', weight=3, tid=0)]], ('e3', 'e25'): [[TemporalEdge(fr='e3', to='e25', weight=3, tid=0)]], ('e3', 'e11'): [[TemporalEdge(fr='e3', to='e11', weight=3, tid=0)]], ('e3', 'e23'): [[TemporalEdge(fr='e3', to='e23', weight=4, tid=0)]], ('e148', 'e143'): [[TemporalEdge(fr='e148', to='e143', weight=3, tid=0)]], ('e678', 'e669'): [[TemporalEdge(fr='e678', to='e669', weight=3, tid=2)]], ('e339', 'e403'): [[TemporalEdge(fr='e339', to='e403', weight=3, tid=1)]], ('e377', 'e381'): [[TemporalEdge(fr='e377', to='e381', weight=3, tid=1)]], ('e464', 'e463'): [[TemporalEdge(fr='e464', to='e463', weight=3, tid=1)]], ('e652', 'e628'): [[TemporalEdge(fr='e652', to='e628', weight=3, tid=2)]], ('e833', 'e646'): [[TemporalEdge(fr='e833', to='e646', weight=3, tid=2)]], ('e833', 'e737'): [[TemporalEdge(fr='e833', to='e737', weight=3, tid=2)]], ('e328', 'e329'): [[TemporalEdge(fr='e328', to='e329', weight=4, tid=1)]], ('e328', 'e367'): [[TemporalEdge(fr='e328', to='e367', weight=3, tid=1)]], ('e328', 'e321'): [[TemporalEdge(fr='e328', to='e321', weight=3, tid=1)]], ('e328', 'e330'): [[TemporalEdge(fr='e328', to='e330', weight=4, tid=1)]], ('e328', 'e331'): [[TemporalEdge(fr='e328', to='e331', weight=3, tid=1)]], ('e328', 'e326'): [[TemporalEdge(fr='e328', to='e326', weight=3, tid=1)]], ('e328', 'e332'): [[TemporalEdge(fr='e328', to='e332', weight=3, tid=1)]], ('e328', 'e333'): [[TemporalEdge(fr='e328', to='e333', weight=4, tid=1)]], ('e328', 'e325'): [[TemporalEdge(fr='e328', to='e325', weight=3, tid=1)]], ('e328', 'e425'): [[TemporalEdge(fr='e328', to='e425', weight=3, tid=1)]], ('e328', 'e327'): [[TemporalEdge(fr='e328', to='e327', weight=4, tid=1)]], ('e328', 'e545'): [[TemporalEdge(fr='e328', to='e545', weight=3, tid=1)]]}\n", + "Temporal s-DAG from e329: 65 nodes, 59 edges\n" + ] + } + ], + "source": [ + "from ash_model.paths import temporal_s_dag\n", + "\n", + "all_tr = all_time_respecting_s_walks(T, s=3)\n", + "print('All time-respecting s-walks (s=3):', all_tr)\n", + "\n", + "# Example: build DAG for a specific hyperedge\n", + "he = list(T.hyperedges())[0]\n", + "dag, sources, targets = temporal_s_dag(T, s=2, start_from=he, stop_at=None, edge=True)\n", + "print(f'Temporal s-DAG from {he}: {dag.number_of_nodes()} nodes, {dag.number_of_edges()} edges')" + ] + }, + { + "cell_type": "markdown", + "id": "be857580", + "metadata": {}, + "source": [ + "## Random walkers\n", + "Random walkers can be simulated on the static s-overlap graph (edge-centric) or under temporal constraints.\n", + "We show probability extraction and a few sampled walks.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "7498c39e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Transition matrix shape: (100, 100)\n", + "Edge index mapping (partial): {0: 0, 3: 1, 9: 2}\n", + "Static sampled walks: [[ 0 12 41 12 60]\n", + " [ 3 70 99 70 54]\n", + " [ 9 25 1 51 32]\n", + " ...\n", + " [83 15 23 93 23]\n", + " [84 47 30 0 10]\n", + " [95 86 22 15 71]]\n" + ] + } + ], + "source": [ + "from ash_model.paths import random_walk_probabilities, random_walks, time_respecting_random_walks\n", + "\n", + "s = 1\n", + "rw_probs, edge_to_index = random_walk_probabilities(T, s, edge=False)\n", + "print('Transition matrix shape:', rw_probs.shape)\n", + "print('Edge index mapping (partial):', dict(list(edge_to_index.items())[:3]))\n", + "\n", + "sampled = random_walks(T, edge=False, num_walks=3, walk_length=5)\n", + "print('Static sampled walks:', sampled)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "3e47bb2a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Temporal sampled walks: [['48' '0' '13' '8' '0']\n", + " ['53' '98' '11' '32' '71']\n", + " ['44' '4' '11' '4' '0']\n", + " ...\n", + " ['86' '0' '5' '9' '13']\n", + " ['8' '10' '12' '56' '12']\n", + " ['86' '37' '9' '5' '60']]\n" + ] + } + ], + "source": [ + "tr_sampled = time_respecting_random_walks(T, s=s, num_walks=3, walk_length=5)\n", + "print('Temporal sampled walks:', tr_sampled)" + ] + }, + { + "cell_type": "markdown", + "id": "e758a314", + "metadata": {}, + "source": [ + "## (Optional) Temporal s-DAG construction\n", + "Set `RUN_ADVANCED = True` to build the temporal s-DAG for the toy temporal instance.\n", + "This can be useful for downstream algorithms (centralities, embeddings).\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "834356a1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Temporal s-DAG nodes/edges: 596 4752\n" + ] + } + ], + "source": [ + "import networkx as nx\n", + "from ash_model.paths import temporal_s_dag\n", + "\n", + "# Build temporal s-DAG for all hyperedges\n", + "s = 2\n", + "dags = []\n", + "for he in T.hyperedges():\n", + " dag, _, _ = temporal_s_dag(T, s, start_from=he, stop_at=None, edge=True)\n", + " dags.append(dag)\n", + "\n", + "G_nx = nx.compose_all(dags)\n", + "print('Temporal s-DAG nodes/edges:', G_nx.number_of_nodes(), G_nx.number_of_edges())" + ] + }, + { + "cell_type": "markdown", + "id": "a5e53156", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.20" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/03-generators.ipynb b/tutorial/03-generators.ipynb new file mode 100644 index 0000000..1dc1a73 --- /dev/null +++ b/tutorial/03-generators.ipynb @@ -0,0 +1,345 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "eee65f85", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "Author: Andrea Failla
\n", + "Python version: 3.9
\n", + "ASH version: 0.1.0
\n", + "Last update: July 2025\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "4b30702a", + "metadata": {}, + "source": [ + "\n", + "# Attributed Stream Hypergraphs (ASH) - Generators" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b27ebfe8", + "metadata": {}, + "outputs": [], + "source": [ + "#!pip install -e ../" + ] + }, + { + "cell_type": "markdown", + "id": "615e6303", + "metadata": {}, + "source": [ + "\n", + "# Table of Contents\n", + "\n", + "- [Introduction](#introduction)\n", + "- [Overview of Generators](#overview)\n", + "- [Random Static Hypergraph](#random-static)\n", + "- [Random Temporal ASH](#random-temporal)\n", + "- [Homophily-driven BA Hypergraph](#homophily-ba)\n", + "- [Comparing Generators](#comparing)\n", + "- [Reproducibility & Seeding](#reproducibility)\n", + "- [Cleanup & Next Steps](#cleanup)\n" + ] + }, + { + "cell_type": "markdown", + "id": "211a440d", + "metadata": {}, + "source": [ + "\n", + "## Introduction\n", + "\n", + "This notebook showcases synthetic data generators included in ASH. These tools help you:\n", + "- Prototype algorithms on controlled hypergraph structures\n", + "- Study effects of attribute homophily & degree bias\n", + "- Produce temporal or static datasets with attribute varieties\n", + "\n", + "We cover three primary generators and how to tune their parameters.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "cea083f0", + "metadata": {}, + "source": [ + "\n", + "## Overview of Generators\n", + "\n", + "| Generator | Function | Key Parameters | Output Type |\n", + "|-----------|----------|----------------|-------------|\n", + "| Random Static | `random_hypergraph` | `num_nodes`, `size_distr`, `node_attrs`, `seed` | Single-snapshot ASH (t=0) |\n", + "| Random Temporal | `random_ash` | `num_nodes`, `size_distr`, `time_steps`, `node_attrs`, `seed` | Multi-snapshot ASH |\n", + "| Homophily BA | `ba_with_homophily` | `num_nodes`, `m`, `homophily_rate`, `minority_size`, `n0`, `size_prob_distr` | Static preferential + homophily |\n", + "\n", + "`size_distr` (static/temporal) maps hyperedge size → count.\n", + "For BA homophily, hyperedge sizes are drawn from a discrete distribution (Pareto by default) with homophily + degree preference when attaching new nodes.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "8793c8ba", + "metadata": {}, + "source": [ + "\n", + "## Random Static Hypergraph (`random_hypergraph`)\n", + "\n", + "Creates a single-snapshot hypergraph at time 0.\n", + "- `size_distr`: {hyperedge_size: count}\n", + "- `node_attrs`: {attr_name: [possible_values]}\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "719cbaf8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nodes: 12 Hyperedges: 10\n", + "Sample hyperedge IDs: ['e3', 'e1', 'e8', 'e10', 'e2']\n", + "Node 0 attrs: {0: {'color': 'red', 'dept': 'A'}}\n" + ] + } + ], + "source": [ + "from ash_model.generators import random_hypergraph\n", + "from ash_model import ASH\n", + "\n", + "static_h = random_hypergraph(\n", + " num_nodes=12,\n", + " size_distr={2:5, 3:3, 4:2},\n", + " node_attrs={'color':['red','blue'], 'dept':['A','B','C']},\n", + " seed=42\n", + ")\n", + "print(\"Nodes:\", static_h.number_of_nodes(), \"Hyperedges:\", static_h.number_of_hyperedges())\n", + "print(\"Sample hyperedge IDs:\", list(static_h.hyperedges())[:5])\n", + "print(\"Node 0 attrs:\", static_h.get_node_attributes(0))" + ] + }, + { + "cell_type": "markdown", + "id": "25308da8", + "metadata": {}, + "source": [ + "\n", + "## Random Temporal ASH (`random_ash`)\n", + "Generates a multi-snapshot ASH with nodes & hyperedges persistent across time range `[0, time_steps-1]`.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "7323bdf9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Snapshots: [0, 1, 2, 3, 4]\n", + "Avg nodes per snapshot: 15.0\n", + "Avg hyperedges per snapshot: 9.0\n" + ] + } + ], + "source": [ + "from ash_model.generators import random_ash\n", + "\n", + "temporal_h = random_ash(\n", + " num_nodes=15,\n", + " size_distr={2:6, 3:4},\n", + " time_steps=5,\n", + " node_attrs={'team':['eng','mkt','sales']},\n", + " seed=7\n", + ")\n", + "print(\"Snapshots:\", temporal_h.temporal_snapshots_ids())\n", + "print(\"Avg nodes per snapshot:\", temporal_h.avg_number_of_nodes())\n", + "print(\"Avg hyperedges per snapshot:\", temporal_h.avg_number_of_hyperedges())" + ] + }, + { + "cell_type": "markdown", + "id": "257fe62f", + "metadata": {}, + "source": [ + "\n", + "## Homophily-driven BA Hypergraph (`ba_with_homophily`)\n", + "Adds nodes sequentially; each new node forms `m` hyperedges with existing nodes.\n", + "Attachment probability blends: (degree preference) × (homophily wrt `color`).\n", + "`minority_size` controls fraction of nodes with minority color.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "88d38c70", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nodes: 40 Hyperedges: 14\n", + "Degree distribution (first 10): [(10, 3), (4, 6), (7, 2), (12, 2), (9, 2), (8, 1), (0, 10), (1, 4), (2, 5), (5, 3)]\n" + ] + } + ], + "source": [ + "from ash_model.generators import ba_with_homophily\n", + "\n", + "homo_h = ba_with_homophily(\n", + " num_nodes=40,\n", + " m=3,\n", + " homophily_rate=0.75,\n", + " minority_size=0.3,\n", + " n0=5\n", + ")\n", + "print(\"Nodes:\", homo_h.number_of_nodes(), \"Hyperedges:\", homo_h.number_of_hyperedges())\n", + "print(\"Degree distribution (first 10):\", list(homo_h.degree_distribution().items())[:10])" + ] + }, + { + "cell_type": "markdown", + "id": "ad2282b0", + "metadata": {}, + "source": [ + "\n", + "## Comparing Generators\n", + "We contrast basic statistics across the three outputs.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a01c66ce", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Static: {'nodes': 12, 'hyperedges': 10, 'avg_deg': 3.0, 'attr_names': ['color', 'dept']}\n", + "Temporal: {'nodes': 15, 'hyperedges': 9, 'avg_deg': 3.0, 'attr_names': ['start', 'end', 'team']}\n", + "Homophily BA: {'nodes': 40, 'hyperedges': 14, 'avg_deg': 3.3333333333333335, 'attr_names': ['color']}\n" + ] + } + ], + "source": [ + "def summary(h):\n", + " return {\n", + " 'nodes': h.number_of_nodes(),\n", + " 'hyperedges': h.number_of_hyperedges(),\n", + " 'avg_deg': sum(h.degree_distribution().values())/len(h.degree_distribution()) if h.degree_distribution() else 0,\n", + " 'attr_names': list(h.list_node_attributes().keys())\n", + " }\n", + "print('Static:', summary(static_h))\n", + "print('Temporal:', summary(temporal_h))\n", + "print('Homophily BA:', summary(homo_h))" + ] + }, + { + "cell_type": "markdown", + "id": "e71786f5", + "metadata": {}, + "source": [ + "\n", + "## Reproducibility & Seeding\n", + "Use `seed` parameter (where available) or set `random.seed()` / NumPy RNG for deterministic runs.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "8ffaa2ef", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Same edge count? True\n" + ] + } + ], + "source": [ + "h1 = random_hypergraph(8, {2:4}, seed=123)\n", + "h2 = random_hypergraph(8, {2:4}, seed=123)\n", + "print(\"Same edge count?\", h1.number_of_hyperedges() == h2.number_of_hyperedges())" + ] + }, + { + "cell_type": "markdown", + "id": "ee24830c", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "id": "3b847f8a", + "metadata": {}, + "source": [ + "\n", + "## Cleanup & Next Steps\n", + "Consider exporting generated datasets using the IO methods shown in the IO notebook, or combining generators to create hybrid scenarios.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "df1dc0ab", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.20" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/04-io.ipynb b/tutorial/04-io.ipynb new file mode 100644 index 0000000..a7a1e18 --- /dev/null +++ b/tutorial/04-io.ipynb @@ -0,0 +1,684 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "de43be1a", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "Author: Andrea Failla
\n", + "Python version: 3.9
\n", + "ASH version: 0.1.0
\n", + "Last update: July 2025\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "d85944af", + "metadata": {}, + "source": [ + "\n", + "# Attributed Stream Hypergraphs (ASH) - IO & Serialization" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d59b11b4", + "metadata": {}, + "outputs": [], + "source": [ + "#!pip install -e ../" + ] + }, + { + "cell_type": "markdown", + "id": "5c82fa49", + "metadata": {}, + "source": [ + "\n", + "# Table of Contents\n", + "\n", + "- [Introduction](#introduction)\n", + "- [Creating an Example ASH](#creating-example-ash)\n", + "- [Writing Node Profiles to CSV](#writing-profiles-csv)\n", + "- [Reading Node Profiles from CSV](#reading-profiles-csv)\n", + "- [Profiles JSONL (read/write + gzip)](#profiles-jsonl)\n", + "- [Hyperedges CSV (structure only)](#hyperedges-csv)\n", + "- [Full ASH JSON (read/write + gzip)](#ash-json)\n", + "- [HIF Format (Hypergraph Interchange Format)](#hif-format)\n", + "- [Integrity & Round-Trip Checks](#integrity-checks)\n", + "- [Best Practices & Tips](#best-practices)\n" + ] + }, + { + "cell_type": "markdown", + "id": "70911afe", + "metadata": {}, + "source": [ + "\n", + "## Introduction\n", + "\n", + "This tutorial covers persistence and interchange of ASH objects and their related data (node profiles and hyperedges).\n", + "You will learn how to:\n", + "\n", + "1. Export/import time-varying node profiles (CSV & JSONL)\n", + "2. Export/import timestamped hyperedges (CSV)\n", + "3. Serialize/deserialize a complete ASH (JSON, optional gzip)\n", + "4. Use the HIF (Hypergraph Interchange Format) exporter/importer for interoperability\n", + "5. Perform integrity checks after round-trips\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "dd1f975c", + "metadata": {}, + "source": [ + "\n", + "## Creating an Example ASH\n", + "\n", + "We'll build a small ASH with a few nodes, temporal node attributes, and hyperedges.\n", + "This instance will be serialized using the different formats.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "c7261ad6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Nodes: [1, 2, 3]\n", + "Hyperedges: ['e3', 'e1', 'e2']\n" + ] + }, + { + "data": { + "text/plain": [ + "'/var/folders/ym/_r1d94191y5bkvmtmz9tv7cw0000gn/T/ash_io_demo_ys24r7li'" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from ash_model import ASH, NProfile\n", + "from ash_model.readwrite import (\n", + " write_profiles_to_csv, read_profiles_from_csv,\n", + " write_profiles_to_jsonl, read_profiles_from_jsonl,\n", + " write_sh_to_csv, read_sh_from_csv,\n", + " write_ash_to_json, read_ash_from_json,\n", + " write_hif, read_hif\n", + ")\n", + "import os, gzip, json, tempfile, shutil\n", + "\n", + "ash = ASH()\n", + "# Node temporal attributes\n", + "ash.add_node(1, start=0, end=2, attr_dict={\"role\": \"admin\", \"score\": 10})\n", + "ash.add_node(1, start=3, attr_dict={\"role\": \"admin\", \"score\": 12})\n", + "ash.add_node(2, start=0, end=3, attr_dict={\"role\": \"user\", \"score\": 5})\n", + "ash.add_node(3, start=1, end=3, attr_dict={\"role\": \"guest\", \"score\": 7})\n", + "\n", + "# Hyperedges with attributes & temporal spans\n", + "ash.add_hyperedge([1,2], start=0, end=1, weight=1.0, kind=\"pair\")\n", + "ash.add_hyperedge([2,3], start=1, end=2, weight=2.0, kind=\"pair\")\n", + "ash.add_hyperedge([1,2,3], start=2, end=3, weight=3.0, kind=\"group\")\n", + "\n", + "print(f\"Nodes: {list(ash.nodes())}\")\n", + "print(f\"Hyperedges: {list(ash.hyperedges())}\")\n", + "\n", + "# Temp working directory for artifacts\n", + "workdir = tempfile.mkdtemp(prefix=\"ash_io_demo_\")\n", + "workdir" + ] + }, + { + "cell_type": "markdown", + "id": "88678df3", + "metadata": {}, + "source": [ + "\n", + "## Writing Node Profiles to CSV\n", + "\n", + "`write_profiles_to_csv` exports one row per (node, timestamp) with all node attributes.\n", + "The header lists attribute names. Types are auto-inferred when reading.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "cc541b06", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "node_id,tid,role,score\n", + "1,0,admin,10\n", + "1,1,admin,10\n", + "1,2,admin,10\n", + "1,3,admin,12\n", + "2,0,user,5\n", + "2,1,user,5\n", + "2,2,user,5\n", + "2,3,user,5\n", + "3,1,guest,7\n", + "3,2,guest,7\n", + "3,3,guest,7\n", + "\n" + ] + } + ], + "source": [ + "profiles_csv = os.path.join(workdir, \"profiles.csv\")\n", + "write_profiles_to_csv(ash, profiles_csv)\n", + "print(open(profiles_csv).read())" + ] + }, + { + "cell_type": "markdown", + "id": "98d921a4", + "metadata": {}, + "source": [ + "\n", + "## Reading Node Profiles from CSV\n", + "\n", + "`read_profiles_from_csv` rebuilds a dict: `{node: {tid: NProfile}}` with type inference.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b20989c1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['node_id,tid,role,score\\n', '1,0,admin,10\\n', '1,1,admin,10\\n', '1,2,admin,10\\n', '1,3,admin,12\\n', '2,0,user,5\\n', '2,1,user,5\\n', '2,2,user,5\\n', '2,3,user,5\\n', '3,1,guest,7\\n', '3,2,guest,7\\n', '3,3,guest,7\\n']\n", + "0 {'role': 'admin', 'score': 10}\n", + "1 {'role': 'admin', 'score': 10}\n", + "2 {'role': 'admin', 'score': 10}\n", + "3 {'role': 'admin', 'score': 12}\n" + ] + } + ], + "source": [ + "profiles_dict = read_profiles_from_csv(profiles_csv)\n", + "# Show reconstructed profile for node 1 over time\n", + "for tid, prof in profiles_dict[1].items():\n", + " print(tid, prof.get_attributes())" + ] + }, + { + "cell_type": "markdown", + "id": "a8e11a03", + "metadata": {}, + "source": [ + "\n", + "## Profiles JSONL (read/write + gzip)\n", + "\n", + "`write_profiles_to_jsonl` appends one JSON object per (node, tid). Optional gzip compression.\n", + "Recommended for large datasets due to streaming-friendly format.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "f0d3cebc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Sample lines:\n", + "{\"node_id\": 1, \"attrs\": {\"role\": \"admin\", \"score\": 10}, \"tid\": 0}\n", + "{\"node_id\": 1, \"attrs\": {\"role\": \"admin\", \"score\": 10}, \"tid\": 1}\n", + "{\"node_id\": 1, \"attrs\": {\"role\": \"admin\", \"score\": 10}, \"tid\": 2}\n", + "Compressed first line: {\"node_id\": 1, \"attrs\": {\"role\": \"admin\", \"score\": 10}, \"tid\": 0}\n", + "Node 2 tids (plain): [0, 1, 2, 3]\n", + "Node 2 tids (gzip): [0, 1, 2, 3]\n" + ] + } + ], + "source": [ + "profiles_jsonl = os.path.join(workdir, \"profiles.jsonl\")\n", + "write_profiles_to_jsonl(ash, profiles_jsonl)\n", + "print(\"Sample lines:\")\n", + "print('\\n'.join(open(profiles_jsonl).read().splitlines()[:3]))\n", + "\n", + "# Gzip compressed\n", + "profiles_jsonl_gz = profiles_jsonl + \".gz\"\n", + "write_profiles_to_jsonl(ash, profiles_jsonl_gz, compress=True)\n", + "with gzip.open(profiles_jsonl_gz, 'rt') as f:\n", + " print(\"Compressed first line:\", f.readline().strip())\n", + "\n", + "# Read back\n", + "jsonl_profiles = read_profiles_from_jsonl(profiles_jsonl)\n", + "jsonl_profiles_gz = read_profiles_from_jsonl(profiles_jsonl_gz, compress=True)\n", + "print(\"Node 2 tids (plain):\", list(jsonl_profiles[2].keys()))\n", + "print(\"Node 2 tids (gzip):\", list(jsonl_profiles_gz[2].keys()))" + ] + }, + { + "cell_type": "markdown", + "id": "4642bc64", + "metadata": {}, + "source": [ + "\n", + "## Hyperedges CSV (structure only)\n", + "\n", + "`write_sh_to_csv` exports each hyperedge presence interval as a row: `n1,n2,...\\tstart,end`.\n", + "Attributes are NOT preserved. Use for lightweight temporal structure dumps.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "e8450996", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "nodes\tstart,end\n", + "1,2,3\t2,3\n", + "1,2\t0,1\n", + "2,3\t1,2\n", + "\n", + "Recovered hyperedges count: 3\n" + ] + } + ], + "source": [ + "hedges_csv = os.path.join(workdir, \"hyperedges.csv\")\n", + "write_sh_to_csv(ash, hedges_csv)\n", + "print(open(hedges_csv).read())\n", + "\n", + "ash_from_hedges = read_sh_from_csv(hedges_csv)\n", + "print(\"Recovered hyperedges count:\", ash_from_hedges.number_of_hyperedges())" + ] + }, + { + "cell_type": "markdown", + "id": "57f8afc5", + "metadata": {}, + "source": [ + "\n", + "## Full ASH JSON (read/write + gzip)\n", + "\n", + "`write_ash_to_json` serializes the entire structure including attributes.\n", + "`read_ash_from_json` reconstructs it (re-adding hyperedges over time).\n", + "Use gzip for large networks.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f418d782", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "JSON size (bytes): 1513\n", + "Gzip JSON size (bytes): 280\n", + "Loaded nodes: 3 Loaded hyperedges: 3\n" + ] + } + ], + "source": [ + "ash_json = os.path.join(workdir, \"ash.json\")\n", + "write_ash_to_json(ash, ash_json)\n", + "print(\"JSON size (bytes):\", os.path.getsize(ash_json))\n", + "\n", + "ash_json_gz = ash_json + \".gz\"\n", + "write_ash_to_json(ash, ash_json_gz, compress=True)\n", + "print(\"Gzip JSON size (bytes):\", os.path.getsize(ash_json_gz))\n", + "\n", + "ash_loaded = read_ash_from_json(ash_json)\n", + "print(\"Loaded nodes:\", ash_loaded.number_of_nodes(), \"Loaded hyperedges:\", ash_loaded.number_of_hyperedges())" + ] + }, + { + "cell_type": "markdown", + "id": "97048512", + "metadata": {}, + "source": [ + "\n", + "## HIF Format (Hypergraph Interchange Format)\n", + "\n", + "`write_hif` exports a structured JSON containing:\n", + "- `incidences`: one record per node–hyperedge membership (with optional weight)\n", + "- `nodes`: each node with time-varying attributes collapsed into (start,end,value) spans plus `_presence`\n", + "- `edges`: hyperedge attributes plus `_presence` intervals\n", + "\n", + "This enables interoperability while preserving temporal semantics compactly.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "df0a80f2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "HIF excerpt:\n", + "{\n", + " \"network-type\": \"undirected\",\n", + " \"metadata\": {\n", + " \"dataset\": \"demo\",\n", + " \"version\": 1\n", + " },\n", + " \"incidences\": [\n", + " {\n", + " \"node\": 1,\n", + " \"edge\": \"e3\",\n", + " \"weight\": 3.0\n", + " },\n", + " {\n", + " \"node\": 2,\n", + " \"edge\": \"e3\",\n", + " \"weight\": 3.0\n", + " },\n", + " {\n", + " \"node\": 3,\n", + " \"edge\": \"e3\",\n", + " \"weight\": 3.0\n", + " },\n", + " {\n", + " \"node\": 1,\n", + " \"edge\": \"e1\"\n", + " },\n", + " {\n", + " \"node\": 2,\n", + " \"edge\": \"e1\"\n", + " },\n", + " {\n", + " \"node\": 2,\n", + " \"edge\": \"e2\",\n", + " \"weight\": 2.0\n", + " },\n", + " {\n", + " \"node\": 3,\n", + " \"edge\": \"e2\",\n", + " \"weight\": 2.0\n", + " }\n", + " ],\n", + " \"nodes\": [\n", + " {\n", + " \"node\": 1,\n", + " \"attrs\": {\n", + " \"role\": [\n", + " [\n", + " 0,\n", + " 3,\n", + " \"admin\"\n", + " ]\n", + " ],\n", + " \"score\": [\n", + " [\n", + " 0,\n", + " 2,\n", + " 10\n", + " ],\n", + " [\n", + " 3,\n", + " 3,\n", + " 12\n", + " ]\n", + " ],\n", + " \"_presence\": [\n", + " [\n", + " 0,\n", + " 3\n", + " ]\n", + " ]\n", + " }\n", + " },\n", + " {\n", + " \"node\": 2,\n", + " \"attrs\": {\n", + " \"role\": [\n", + " [\n", + " 0,\n", + " 3,\n", + " \"user\"\n", + " ]\n", + " ],\n", + " \"score\": [\n", + " [\n", + " 0,\n", + " 3,\n", + " 5\n", + " ]\n", + " ],\n", + " \"_presence\": [\n", + " [\n", + " 0,\n", + " 3\n", + " ]\n", + " ]\n", + " }\n", + " },\n", + " {\n", + " \"node\": 3,\n", + " \"attrs\": {\n", + " \"role\": [\n", + " [\n", + " 1,\n", + " 3,\n", + " \"guest\"\n", + " ]\n", + " ],\n", + " \"score\": [\n", + " [\n", + " 1,\n", + " 3,\n", + " 7\n", + " ]\n", + " ],\n", + " \"_presence\": [\n", + " [\n", + " 1,\n", + " 3\n", + " ]\n", + " ]\n", + " }\n", + " }\n", + " ],\n", + " \"edges\": [\n", + " {\n", + " \"edge\": \"e3\",\n", + " \"attrs\": {\n", + " \"weight\": 3.0,\n", + " \"kind\": \"group\",\n", + " \"_presence\": [\n", + " [\n", + " 2,\n", + " 3\n", + " ]\n", + " ]\n", + " }\n", + " },\n", + " {\n", + " \"edge\": \"e1\",\n", + " \"attrs\": {\n", + " \"weight\": 1.0,\n", + " \"kind\": \"pair\",\n", + " \"_presence\": [\n", + " [\n", + " 0,\n", + " 1\n", + " ]\n", + " ]\n", + " }\n", + " },\n", + " {\n", + " \"edge\": \"e2\",\n", + " \"attrs\": {\n", + " \"weight\": 2.0,\n", + " \"kind\": \"pair\",\n", + " \"_presence\": [\n", + " [\n", + " 1,\n", + " 2\n", + " ]\n", + " ]\n", + " }\n", + " }\n", + " ]\n", + "}\n", + "HIF loaded nodes: 3 hyperedges: 3\n" + ] + } + ], + "source": [ + "hif_path = os.path.join(workdir, \"ash.hif.json\")\n", + "write_hif(ash, hif_path, metadata={\"dataset\": \"demo\", \"version\": 1})\n", + "print(\"HIF excerpt:\")\n", + "print('\\n'.join(open(hif_path).read().splitlines()))\n", + "\n", + "ash_hif_loaded = read_hif(hif_path)\n", + "print(\"HIF loaded nodes:\", ash_hif_loaded.number_of_nodes(), \"hyperedges:\", ash_hif_loaded.number_of_hyperedges())" + ] + }, + { + "cell_type": "markdown", + "id": "5452f76f", + "metadata": {}, + "source": [ + "\n", + "## Integrity & Round-Trip Checks\n", + "\n", + "We compare basic statistics (counts, attribute sets) after reloading from different formats.\n", + "For deeper checks you could diff presence intervals & attribute timelines.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "7b46877e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original: {'nodes': 3, 'hyperedges': 3, 'node_attrs': ['role', 'score'], 'hedge_attrs': ['kind', 'weight']}\n", + "From hedges CSV (no attrs): {'nodes': 3, 'hyperedges': 3, 'node_attrs': [], 'hedge_attrs': ['weight']}\n", + "From JSON: {'nodes': 3, 'hyperedges': 3, 'node_attrs': ['role', 'score'], 'hedge_attrs': ['kind', 'weight']}\n", + "From HIF: {'nodes': 3, 'hyperedges': 3, 'node_attrs': ['role', 'score'], 'hedge_attrs': ['kind', 'weight']}\n" + ] + } + ], + "source": [ + "def summary(h):\n", + " return {\n", + " 'nodes': h.number_of_nodes(),\n", + " 'hyperedges': h.number_of_hyperedges(),\n", + " 'node_attrs': sorted(h.list_node_attributes().keys()),\n", + " 'hedge_attrs': sorted(h.list_hyperedge_attributes().keys())\n", + " }\n", + "\n", + "print('Original:', summary(ash))\n", + "print('From hedges CSV (no attrs):', summary(ash_from_hedges))\n", + "print('From JSON:', summary(ash_loaded))\n", + "print('From HIF:', summary(ash_hif_loaded))" + ] + }, + { + "cell_type": "markdown", + "id": "430e3bea", + "metadata": {}, + "source": [ + "\n", + "## Best Practices & Tips\n", + "\n", + "- Use JSONL (optionally gzipped) for very large node profile timelines (streaming friendly).\n", + "- Use full JSON (gzip) when you need a faithful snapshot including attributes.\n", + "- Use HIF for interoperability / archival: compact temporal attribute encoding.\n", + "- Hyperedges CSV is lossy (drops attributes) — only for quick topology experiments.\n", + "- Always validate round-trip with basic stats (& optionally invariants like degree distribution).\n", + "- Keep metadata (e.g. preprocessing parameters) inside HIF `metadata`.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "4cca95e7", + "metadata": {}, + "outputs": [], + "source": [ + "# Optional: cleanup temporary directory when done\n", + "shutil.rmtree(workdir)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bc314359", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.20" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/05-multiego.ipynb b/tutorial/05-multiego.ipynb new file mode 100644 index 0000000..3f1c3ee --- /dev/null +++ b/tutorial/05-multiego.ipynb @@ -0,0 +1,902 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "807ca3be", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "Author: Andrea Failla
\n", + "Python version: 3.9
\n", + "ASH version: 1.0.0
\n", + "Last update: November 2025\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "e03eddd2", + "metadata": {}, + "source": [ + "\n", + "# Multi-Ego Networks" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "e1900778", + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "sys.path.insert(0, '../')" + ] + }, + { + "cell_type": "markdown", + "id": "3cbc3172", + "metadata": {}, + "source": [ + "\n", + "# Table of Contents\n", + "\n", + " - [Introduction](#introduction)\n", + " - [Basic Concepts](#basic-concepts)\n", + " - [What is an Ego Network?](#what-is-an-ego-network)\n", + " - [What is a Multi-Ego Network?](#what-is-a-multi-ego-network)\n", + " - [Extracting Multi-Ego Networks](#extracting-multi-ego-networks)\n", + " - [Standard Multi-Ego Network](#standard-multi-ego-network)\n", + " - [Fractured Multi-Ego Network](#fractured-multi-ego-network)\n", + " - [Core Multi-Ego Network](#core-multi-ego-network)\n", + " - [Temporal Multi-Ego Networks](#temporal-multi-ego-networks)\n", + " - [Comparing Multi-Ego Networks](#comparing-multi-ego-networks)\n", + " - [Jaccard Similarity](#jaccard-similarity)\n", + " - [Minimum Overlapping Similarity](#minimum-overlapping-similarity)\n", + " - [Delta Similarity](#delta-similarity)\n", + " - [Practical Examples](#practical-examples)" + ] + }, + { + "cell_type": "markdown", + "id": "c80f6efd", + "metadata": {}, + "source": [ + "\n", + "## Introduction\n", + "\n", + "Multi-Ego Networks extend the classical concept of ego networks from simple graphs to temporal hypergraphs. While a traditional ego network focuses on a single node and its immediate neighbors, Multi-Ego Networks allow us to study the local structure around **multiple focal nodes** simultaneously, providing a richer understanding of group-centric patterns in higher-order interactions.\n", + "\n", + "This tutorial will guide you through the extraction, analysis, and comparison of Multi-Ego Networks in ASH.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "bfa04e32", + "metadata": {}, + "source": [ + "\n", + "## Basic Concepts\n", + "\n", + "\n", + "### What is an Ego Network?\n", + "\n", + "An **ego network** is a subnetwork centered around a single focal node (the \"ego\"). In a simple graph, it consists of:\n", + "- The ego node itself\n", + "- All nodes directly connected to the ego (called \"alters\")\n", + "- All edges between these nodes\n", + "\n", + "In a hypergraph, the ego network consists of all hyperedges that contain the ego node. This is accessible in ASH via the `star()` method:\n", + "\n", + "```python\n", + "h = ASH()\n", + "# ... add hyperedges ...\n", + "ego_edges = h.star(node_id=1, start=0, end=5)\n", + "```\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "b62b3488", + "metadata": {}, + "source": [ + "\n", + "### What is a Multi-Ego Network?\n", + "\n", + "A **Multi-Ego Network** generalizes the ego network concept to **multiple focal nodes** (egos). Instead of centering the analysis on a single node, we consider a set of nodes U = {u₁, u₂, ..., uₖ} and extract the local structure around all of them.\n", + "\n", + "The `multiego` module in ASH provides three variants:\n", + "\n", + "1. **Standard Multi-Ego**: All hyperedges containing **at least one** node from U\n", + "2. **Fractured Multi-Ego**: All hyperedges containing **at least α·|U|** nodes from U\n", + "3. **Core Multi-Ego**: All hyperedges where nodes from U represent **at least β fraction** of the hyperedge size\n", + "\n", + "These variants allow fine-grained control over what constitutes \"local structure\" for a group of nodes.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "20d5fa1f", + "metadata": {}, + "source": [ + "\n", + "## Extracting Multi-Ego Networks\n", + "\n", + "Let's create a sample temporal hypergraph and explore the different types of Multi-Ego Networks." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2db2be13", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hypergraph created with 6 nodes and 8 hyperedges\n", + "Time range: [0, 1, 2]\n" + ] + } + ], + "source": [ + "from ash_model import ASH\n", + "from ash_model.multiego import (\n", + " get_multiego,\n", + " get_fractured_multiego,\n", + " get_core_multiego\n", + ")\n", + "\n", + "# Create a temporal hypergraph\n", + "h = ASH()\n", + "\n", + "# Add hyperedges at different time points\n", + "# Time 0\n", + "h.add_hyperedge([1, 2, 3], start=0, end=0)\n", + "h.add_hyperedge([2, 3, 4], start=0, end=0)\n", + "h.add_hyperedge([1, 4, 5], start=0, end=0)\n", + "\n", + "# Time 1\n", + "h.add_hyperedge([1, 2, 5], start=1, end=1)\n", + "h.add_hyperedge([3, 4, 5, 6], start=1, end=1)\n", + "h.add_hyperedge([1, 3], start=1, end=1)\n", + "\n", + "# Time 2\n", + "h.add_hyperedge([2, 4, 6], start=2, end=2)\n", + "h.add_hyperedge([1, 2, 3, 4], start=2, end=2)\n", + "\n", + "print(f\"Hypergraph created with {h.number_of_nodes()} nodes and {h.number_of_hyperedges()} hyperedges\")\n", + "print(f\"Time range: {h.temporal_snapshots_ids()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "7e349270", + "metadata": {}, + "source": [ + "\n", + "### Standard Multi-Ego Network\n", + "\n", + "The standard Multi-Ego Network includes all hyperedges that contain **at least one** node from the ego set U.\n", + "\n", + "**Use case**: Finding all interactions where at least one member of a team/group participates." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "34f42d0f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Multi-Ego Network for U={1, 2, 3} at time 0:\n", + " 1. {1, 2, 3}\n", + " 2. {1, 4, 5}\n", + " 3. {2, 3, 4}\n", + "\n", + "Multi-Ego Network for U={1, 2, 3} in window [0,1]:\n", + " 1. {1, 2, 3}\n", + " 2. {1, 3}\n", + " 3. {1, 4, 5}\n", + " 4. {2, 3, 4}\n", + " 5. {3, 4, 5, 6}\n", + " 6. {1, 2, 5}\n", + "\n", + "Total hyperedges in Multi-Ego: 6\n" + ] + } + ], + "source": [ + "# Define our ego set\n", + "U = {1, 2, 3}\n", + "\n", + "# Extract Multi-Ego Network at time 0\n", + "multiego_t0 = get_multiego(h, U, start=0)\n", + "print(f\"Multi-Ego Network for U={U} at time 0:\")\n", + "for i, edge in enumerate(multiego_t0, 1):\n", + " print(f\" {i}. {edge}\")\n", + "\n", + "# Extract Multi-Ego Network for time window [0, 1]\n", + "multiego_window = get_multiego(h, U, start=0, end=1)\n", + "print(f\"\\nMulti-Ego Network for U={U} in window [0,1]:\")\n", + "for i, edge in enumerate(multiego_window, 1):\n", + " print(f\" {i}. {edge}\")\n", + "\n", + "print(f\"\\nTotal hyperedges in Multi-Ego: {len(multiego_window)}\")" + ] + }, + { + "cell_type": "markdown", + "id": "9b316473", + "metadata": {}, + "source": [ + "\n", + "### Fractured Multi-Ego Network\n", + "\n", + "The Fractured Multi-Ego Network includes hyperedges where **at least α·|U|** nodes from U are present. The parameter α ∈ (0, 1] controls the \"strength\" of the ego presence.\n", + "\n", + "**Use case**: Finding interactions where a significant fraction of a team is present (e.g., meetings with at least 50% of core team members)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "aba05a56", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fractured Multi-Ego (α=0.33) for U={1, 2, 3}:\n", + " {1, 2, 3}\n", + " {1, 3}\n", + " {1, 4, 5}\n", + " {2, 3, 4}\n", + " {3, 4, 5, 6}\n", + " {1, 2, 5}\n", + "\n", + "Fractured Multi-Ego (α=0.67) for U={1, 2, 3}:\n", + " {1, 2, 3}\n", + "\n", + "Fractured Multi-Ego (α=1.0) for U={1, 2, 3}:\n", + " {1, 2, 3}\n", + "\n", + "Summary: α=0.33 → 6 edges, α=0.67 → 1 edges, α=1.0 → 1 edges\n" + ] + } + ], + "source": [ + "# Extract Fractured Multi-Ego with different alpha values\n", + "U = {1, 2, 3}\n", + "\n", + "# alpha = 0.33: at least 1 node from U (33% of 3)\n", + "fractured_033 = get_fractured_multiego(h, U, start=0, end=1, alpha=0.33)\n", + "print(f\"Fractured Multi-Ego (α=0.33) for U={U}:\")\n", + "for edge in fractured_033:\n", + " print(f\" {edge}\")\n", + "\n", + "# alpha = 0.67: at least 2 nodes from U (67% of 3)\n", + "fractured_067 = get_fractured_multiego(h, U, start=0, end=1, alpha=0.67)\n", + "print(f\"\\nFractured Multi-Ego (α=0.67) for U={U}:\")\n", + "for edge in fractured_067:\n", + " print(f\" {edge}\")\n", + "\n", + "# alpha = 1.0: all nodes from U must be present\n", + "fractured_100 = get_fractured_multiego(h, U, start=0, end=1, alpha=1.0)\n", + "print(f\"\\nFractured Multi-Ego (α=1.0) for U={U}:\")\n", + "for edge in fractured_100:\n", + " print(f\" {edge}\")\n", + "\n", + "print(f\"\\nSummary: α=0.33 → {len(fractured_033)} edges, α=0.67 → {len(fractured_067)} edges, α=1.0 → {len(fractured_100)} edges\")" + ] + }, + { + "cell_type": "markdown", + "id": "c80565e4", + "metadata": {}, + "source": [ + "\n", + "### Core Multi-Ego Network\n", + "\n", + "The Core Multi-Ego Network includes hyperedges where nodes from U represent **at least β fraction** of the hyperedge size. The parameter β ∈ (0, 1] controls how \"dominated\" the hyperedge must be by the ego set.\n", + "\n", + "**Use case**: Finding small interactions where the ego group dominates (e.g., committees where core members are the majority)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "ec3ecf8a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Core Multi-Ego (β=0.5) for U={1, 2, 3}:\n", + " {1, 2, 3} (U contributes 3/3 nodes = 100.0%)\n", + " {1, 3} (U contributes 2/2 nodes = 100.0%)\n", + " {2, 3, 4} (U contributes 2/3 nodes = 66.7%)\n", + " {1, 2, 5} (U contributes 2/3 nodes = 66.7%)\n", + "\n", + "Core Multi-Ego (β=0.75) for U={1, 2, 3}:\n", + " {1, 2, 3} (U contributes 3/3 nodes = 100.0%)\n", + " {1, 3} (U contributes 2/2 nodes = 100.0%)\n", + "\n", + "Summary: β=0.5 → 4 edges, β=0.75 → 2 edges\n" + ] + } + ], + "source": [ + "# Extract Core Multi-Ego with different beta values\n", + "U = {1, 2, 3}\n", + "\n", + "# beta = 0.5: U nodes are at least 50% of the hyperedge\n", + "core_050 = get_core_multiego(h, U, start=0, end=1, beta=0.5)\n", + "print(f\"Core Multi-Ego (β=0.5) for U={U}:\")\n", + "for edge in core_050:\n", + " u_in_edge = len(set(edge).intersection(U))\n", + " print(f\" {edge} (U contributes {u_in_edge}/{len(edge)} nodes = {u_in_edge/len(edge):.1%})\")\n", + "\n", + "# beta = 0.75: U nodes are at least 75% of the hyperedge\n", + "core_075 = get_core_multiego(h, U, start=0, end=1, beta=0.75)\n", + "print(f\"\\nCore Multi-Ego (β=0.75) for U={U}:\")\n", + "for edge in core_075:\n", + " u_in_edge = len(set(edge).intersection(U))\n", + " print(f\" {edge} (U contributes {u_in_edge}/{len(edge)} nodes = {u_in_edge/len(edge):.1%})\")\n", + "\n", + "print(f\"\\nSummary: β=0.5 → {len(core_050)} edges, β=0.75 → {len(core_075)} edges\")" + ] + }, + { + "cell_type": "markdown", + "id": "97a51171", + "metadata": {}, + "source": [ + "\n", + "## Temporal Multi-Ego Networks\n", + "\n", + "One of the key strengths of Multi-Ego Networks in ASH is the ability to study how the local structure around a group evolves over time." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "1cee1c30", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Multi-Ego Network evolution for U={1, 2, 3}:\n", + "\n", + "Time 0: 3 hyperedges\n", + " {1, 2, 3}\n", + " {1, 4, 5}\n", + " {2, 3, 4}\n", + "\n", + "Time 1: 3 hyperedges\n", + " {1, 3}\n", + " {3, 4, 5, 6}\n", + " {1, 2, 5}\n", + "\n", + "Time 2: 2 hyperedges\n", + " {1, 2, 3, 4}\n", + " {2, 4, 6}\n", + "\n", + "Early snapshot (t=0): 3 hyperedges\n", + "Late snapshot (t=2): 2 hyperedges\n" + ] + } + ], + "source": [ + "# Track Multi-Ego evolution over time\n", + "U = {1, 2, 3}\n", + "\n", + "print(f\"Multi-Ego Network evolution for U={U}:\\n\")\n", + "\n", + "for t in h.temporal_snapshots_ids():\n", + " multiego_t = get_multiego(h, U, start=t)\n", + " print(f\"Time {t}: {len(multiego_t)} hyperedges\")\n", + " for edge in multiego_t:\n", + " print(f\" {edge}\")\n", + " print()\n", + "\n", + "# Compare snapshots\n", + "multiego_early = get_multiego(h, U, start=0)\n", + "multiego_late = get_multiego(h, U, start=2)\n", + "\n", + "print(f\"Early snapshot (t=0): {len(multiego_early)} hyperedges\")\n", + "print(f\"Late snapshot (t=2): {len(multiego_late)} hyperedges\")" + ] + }, + { + "cell_type": "markdown", + "id": "ffdea25b", + "metadata": {}, + "source": [ + "\n", + "## Comparing Multi-Ego Networks\n", + "\n", + "The `multiego` module provides three similarity measures to compare Multi-Ego Networks across time, different ego sets, or different conditions." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "d635245f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Comparing Multi-Ego Networks for U={1, 2, 3} across time:\n", + "\n", + "Time 0: [{1, 2, 3}, {1, 4, 5}, {2, 3, 4}]\n", + "Time 1: [{1, 3}, {3, 4, 5, 6}, {1, 2, 5}]\n", + "Time 2: [{1, 2, 3, 4}, {2, 4, 6}]\n" + ] + } + ], + "source": [ + "from ash_model.multiego import (\n", + " jaccard_similarity,\n", + " minimum_overlapping_similarity,\n", + " delta_similarity\n", + ")\n", + "\n", + "# Get Multi-Ego Networks at different times\n", + "U = {1, 2, 3}\n", + "multiego_t0 = get_multiego(h, U, start=0)\n", + "multiego_t1 = get_multiego(h, U, start=1)\n", + "multiego_t2 = get_multiego(h, U, start=2)\n", + "\n", + "print(f\"Comparing Multi-Ego Networks for U={U} across time:\\n\")\n", + "print(f\"Time 0: {multiego_t0}\")\n", + "print(f\"Time 1: {multiego_t1}\")\n", + "print(f\"Time 2: {multiego_t2}\")" + ] + }, + { + "cell_type": "markdown", + "id": "95d10c7f", + "metadata": {}, + "source": [ + "\n", + "### Jaccard Similarity\n", + "\n", + "Jaccard similarity measures the overlap as: **|intersection| / |union|**\n", + "\n", + "This is a strict measure - hyperedges must match exactly (same set of nodes)." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "8d4cc1a5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Jaccard similarity:\n", + " t0 vs t1: 0.000\n", + " t1 vs t2: 0.000\n", + " t0 vs t2: 0.000\n", + "\n", + "→ Low overlap - the Multi-Ego structure changed significantly\n" + ] + } + ], + "source": [ + "# Compute Jaccard similarity between time snapshots\n", + "jac_01 = jaccard_similarity(multiego_t0, multiego_t1)\n", + "jac_12 = jaccard_similarity(multiego_t1, multiego_t2)\n", + "jac_02 = jaccard_similarity(multiego_t0, multiego_t2)\n", + "\n", + "print(f\"Jaccard similarity:\")\n", + "print(f\" t0 vs t1: {jac_01:.3f}\")\n", + "print(f\" t1 vs t2: {jac_12:.3f}\")\n", + "print(f\" t0 vs t2: {jac_02:.3f}\")\n", + "\n", + "# Interpretation\n", + "if jac_01 > 0.5:\n", + " print(\"\\n→ High overlap between consecutive snapshots\")\n", + "else:\n", + " print(\"\\n→ Low overlap - the Multi-Ego structure changed significantly\")" + ] + }, + { + "cell_type": "markdown", + "id": "aef70df0", + "metadata": {}, + "source": [ + "\n", + "### Minimum Overlapping Similarity\n", + "\n", + "Minimum overlapping similarity measures: **|intersection| / min(|set1|, |set2|)**\n", + "\n", + "This is more lenient than Jaccard - it normalizes by the smaller set." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "0e69bdbf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Minimum overlapping similarity:\n", + " t0 vs t1: 0.000\n", + " t1 vs t2: 0.000\n", + " t0 vs t2: 0.000\n", + "\n", + "Comparison with Jaccard:\n", + " Jaccard(t0,t1)=0.000 vs Overlap(t0,t1)=0.000\n", + " → Overlap is always ≥ Jaccard (more lenient)\n" + ] + } + ], + "source": [ + "# Compute minimum overlapping similarity\n", + "overlap_01 = minimum_overlapping_similarity(multiego_t0, multiego_t1)\n", + "overlap_12 = minimum_overlapping_similarity(multiego_t1, multiego_t2)\n", + "overlap_02 = minimum_overlapping_similarity(multiego_t0, multiego_t2)\n", + "\n", + "print(f\"Minimum overlapping similarity:\")\n", + "print(f\" t0 vs t1: {overlap_01:.3f}\")\n", + "print(f\" t1 vs t2: {overlap_12:.3f}\")\n", + "print(f\" t0 vs t2: {overlap_02:.3f}\")\n", + "\n", + "print(f\"\\nComparison with Jaccard:\")\n", + "print(f\" Jaccard(t0,t1)={jac_01:.3f} vs Overlap(t0,t1)={overlap_01:.3f}\")\n", + "print(f\" → Overlap is always ≥ Jaccard (more lenient)\")" + ] + }, + { + "cell_type": "markdown", + "id": "7895de1e", + "metadata": {}, + "source": [ + "\n", + "### Delta Similarity\n", + "\n", + "Delta similarity is a **soft matching** measure that considers node-level overlap between hyperedges. It finds the best pairing between hyperedges based on their node similarity.\n", + "\n", + "This is useful when hyperedges don't match exactly but share many nodes." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "edbb7825", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Delta similarity (soft matching):\n", + " t0 vs t1: 0.522\n", + " t1 vs t2: 0.300\n", + " t0 vs t2: 0.417\n", + "\n", + "Comparison of all three measures (t0 vs t1):\n", + " Jaccard: 0.000 (strict)\n", + " Min Overlap: 0.000 (lenient)\n", + " Delta: 0.522 (soft matching)\n" + ] + } + ], + "source": [ + "# Compute delta similarity\n", + "delta_01 = delta_similarity(multiego_t0, multiego_t1)\n", + "delta_12 = delta_similarity(multiego_t1, multiego_t2)\n", + "delta_02 = delta_similarity(multiego_t0, multiego_t2)\n", + "\n", + "print(f\"Delta similarity (soft matching):\")\n", + "print(f\" t0 vs t1: {delta_01:.3f}\")\n", + "print(f\" t1 vs t2: {delta_12:.3f}\")\n", + "print(f\" t0 vs t2: {delta_02:.3f}\")\n", + "\n", + "print(f\"\\nComparison of all three measures (t0 vs t1):\")\n", + "print(f\" Jaccard: {jac_01:.3f} (strict)\")\n", + "print(f\" Min Overlap: {overlap_01:.3f} (lenient)\")\n", + "print(f\" Delta: {delta_01:.3f} (soft matching)\")" + ] + }, + { + "cell_type": "markdown", + "id": "b275657c", + "metadata": {}, + "source": [ + "\n", + "## Practical Examples\n", + "\n", + "Let's explore some practical scenarios where Multi-Ego Networks are useful." + ] + }, + { + "cell_type": "markdown", + "id": "2b6c6bf9", + "metadata": {}, + "source": [ + "### Example 1: Comparing Different Ego Sets\n", + "\n", + "How does the local structure differ for different groups of nodes?" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "8904f6d3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Multi-Ego for U1={1, 2, 3}: 8 hyperedges\n", + "Multi-Ego for U2={4, 5, 6}: 6 hyperedges\n", + "\n", + "Similarity between the two groups: 0.750\n", + "→ The two groups have overlapping neighborhoods\n" + ] + } + ], + "source": [ + "# Define two different ego sets\n", + "U1 = {1, 2, 3} # First group\n", + "U2 = {4, 5, 6} # Second group\n", + "\n", + "# Get their Multi-Ego Networks\n", + "multiego_U1 = get_multiego(h, U1, start=0, end=2)\n", + "multiego_U2 = get_multiego(h, U2, start=0, end=2)\n", + "\n", + "print(f\"Multi-Ego for U1={U1}: {len(multiego_U1)} hyperedges\")\n", + "print(f\"Multi-Ego for U2={U2}: {len(multiego_U2)} hyperedges\")\n", + "\n", + "# Compare the two groups\n", + "sim = jaccard_similarity(multiego_U1, multiego_U2)\n", + "print(f\"\\nSimilarity between the two groups: {sim:.3f}\")\n", + "\n", + "if sim < 0.2:\n", + " print(\"→ The two groups operate in largely separate regions of the hypergraph\")\n", + "else:\n", + " print(\"→ The two groups have overlapping neighborhoods\")" + ] + }, + { + "cell_type": "markdown", + "id": "47c75ca3", + "metadata": {}, + "source": [ + "### Example 2: Tracking Group Cohesion Over Time\n", + "\n", + "How cohesive is a group? Do they participate in many hyperedges together?" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "49919ffa", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Group cohesion analysis for U={1, 2, 3}:\n", + "\n", + "Time 0:\n", + " Any member: 3 hyperedges\n", + " Multiple members (≥67%): 1 hyperedges\n", + " Dominant (≥50%): 2 hyperedges\n", + " Cohesion ratio: 0.33\n", + "\n", + "Time 1:\n", + " Any member: 3 hyperedges\n", + " Multiple members (≥67%): 0 hyperedges\n", + " Dominant (≥50%): 2 hyperedges\n", + " Cohesion ratio: 0.00\n", + "\n", + "Time 2:\n", + " Any member: 2 hyperedges\n", + " Multiple members (≥67%): 1 hyperedges\n", + " Dominant (≥50%): 1 hyperedges\n", + " Cohesion ratio: 0.50\n", + "\n", + "Interpretation:\n", + " High cohesion ratio → Group members often appear together\n", + " Low cohesion ratio → Group members participate independently\n" + ] + } + ], + "source": [ + "# Define a group and track its cohesion\n", + "U = {1, 2, 3}\n", + "\n", + "print(f\"Group cohesion analysis for U={U}:\\n\")\n", + "\n", + "for t in h.temporal_snapshots_ids():\n", + " # Standard: any member participates\n", + " standard = get_multiego(h, U, start=t)\n", + " \n", + " # Fractured: at least 2 members (67%)\n", + " fractured = get_fractured_multiego(h, U, start=t, alpha=0.67)\n", + " \n", + " # Core: members dominate (>50%)\n", + " core = get_core_multiego(h, U, start=t, beta=0.5)\n", + " \n", + " cohesion_ratio = len(fractured) / len(standard) if len(standard) > 0 else 0\n", + " \n", + " print(f\"Time {t}:\")\n", + " print(f\" Any member: {len(standard)} hyperedges\")\n", + " print(f\" Multiple members (≥67%): {len(fractured)} hyperedges\")\n", + " print(f\" Dominant (≥50%): {len(core)} hyperedges\")\n", + " print(f\" Cohesion ratio: {cohesion_ratio:.2f}\")\n", + " print()\n", + "\n", + "print(\"Interpretation:\")\n", + "print(\" High cohesion ratio → Group members often appear together\")\n", + "print(\" Low cohesion ratio → Group members participate independently\")" + ] + }, + { + "cell_type": "markdown", + "id": "ece005c4", + "metadata": {}, + "source": [ + "### Example 3: Identifying Group Influence Zones\n", + "\n", + "Where does a group have the most influence? Find hyperedges dominated by the group." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "75d6b8ad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hyperedges dominated by U={1, 2, 3} (β≥0.66):\n", + "\n", + " {1, 2, 3}\n", + " → From U: {1, 2, 3}\n", + " → Others: none\n", + " → U contribution: 3/3 = 100.0%\n", + "\n", + " {1, 3}\n", + " → From U: {1, 3}\n", + " → Others: none\n", + " → U contribution: 2/2 = 100.0%\n", + "\n", + " {1, 2, 3, 4}\n", + " → From U: {1, 2, 3}\n", + " → Others: {4}\n", + " → U contribution: 3/4 = 75.0%\n", + "\n", + " {2, 3, 4}\n", + " → From U: {2, 3}\n", + " → Others: {4}\n", + " → U contribution: 2/3 = 66.7%\n", + "\n", + " {1, 2, 5}\n", + " → From U: {1, 2}\n", + " → Others: {5}\n", + " → U contribution: 2/3 = 66.7%\n", + "\n", + "Total influence zones: 5 hyperedges\n" + ] + } + ], + "source": [ + "# Find where the group dominates\n", + "U = {1, 2, 3}\n", + "\n", + "# Get Core Multi-Ego with high beta\n", + "dominated = get_core_multiego(h, U, start=0, end=2, beta=0.66)\n", + "\n", + "print(f\"Hyperedges dominated by U={U} (β≥0.66):\\n\")\n", + "\n", + "for edge in dominated:\n", + " u_nodes = set(edge).intersection(U)\n", + " other_nodes = set(edge) - U\n", + " \n", + " print(f\" {edge}\")\n", + " print(f\" → From U: {u_nodes}\")\n", + " print(f\" → Others: {other_nodes if other_nodes else 'none'}\")\n", + " print(f\" → U contribution: {len(u_nodes)}/{len(edge)} = {len(u_nodes)/len(edge):.1%}\")\n", + " print()\n", + "\n", + "print(f\"Total influence zones: {len(dominated)} hyperedges\")" + ] + }, + { + "cell_type": "markdown", + "id": "33d63b2f", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "Multi-Ego Networks provide powerful tools for analyzing group-centric structures in temporal hypergraphs:\n", + "\n", + "**Key Concepts:**\n", + "- **Standard Multi-Ego**: Captures all interactions involving any group member\n", + "- **Fractured Multi-Ego**: Requires minimum group presence (α·|U| members)\n", + "- **Core Multi-Ego**: Requires group dominance (β fraction of hyperedge)\n", + "\n", + "**Similarity Measures:**\n", + "- **Jaccard**: Strict matching (exact hyperedge equality)\n", + "- **Minimum Overlapping**: Lenient matching (normalized by smaller set)\n", + "- **Delta**: Soft matching (node-level similarity)\n", + "\n", + "**Applications:**\n", + "- Tracking group evolution over time\n", + "- Comparing different groups\n", + "- Measuring group cohesion\n", + "- Identifying influence zones\n", + "- Studying collaborative patterns\n", + "\n", + "**Next Steps:**\n", + "- Explore the [walks tutorial](02-walks.ipynb) for path-based analysis\n", + "- Check the [attribute analysis tutorial](01-attribute_analysis.ipynb) for combining Multi-Ego with node attributes\n", + "- See the [generators tutorial](03-generators.ipynb) for creating synthetic hypergraphs\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "79d1b2d0", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/tutorial/06-segregation.ipynb b/tutorial/06-segregation.ipynb new file mode 100644 index 0000000..fe507c5 --- /dev/null +++ b/tutorial/06-segregation.ipynb @@ -0,0 +1,994 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "3be5b253", + "metadata": {}, + "source": [ + "\n", + "\n", + "\n", + "\n", + "Author: Andrea Failla
\n", + "Python version: 3.9
\n", + "ASH version: 1.0.0
\n", + "Last update: November 2025\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "475d8108", + "metadata": {}, + "source": [ + "\n", + "# Hypergraph Segregation Analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "9f150a4a", + "metadata": {}, + "outputs": [], + "source": [ + "import sys\n", + "sys.path.insert(0, '../')" + ] + }, + { + "cell_type": "markdown", + "id": "12dde42e", + "metadata": {}, + "source": [ + "\n", + "# Table of Contents\n", + "\n", + " - [Introduction](#introduction)\n", + " - [What is Segregation in Hypergraphs?](#what-is-segregation-in-hypergraphs)\n", + " - [Random Walk Hypergraph Segregation (RWHS)](#random-walk-hypergraph-segregation-rwhs)\n", + " - [Meet-wise RWHS](#meet-wise-rwhs)\n", + " - [Jump-wise RWHS](#jump-wise-rwhs)\n", + " - [Static RWHS](#static-rwhs)\n", + " - [Basic Example](#basic-example)\n", + " - [Comparing Methods](#comparing-methods)\n", + " - [Effect of Random Walk Parameters](#effect-of-random-walk-parameters)\n", + " - [Temporal RWHS](#temporal-rwhs)\n", + " - [Practical Examples](#practical-examples)\n", + " - [Measuring Attribute Mixing](#measuring-attribute-mixing)\n", + " - [Comparing Segregation Across Time](#comparing-segregation-across-time)\n", + " - [Parameter Tuning](#parameter-tuning)\n", + " - [References](#references)" + ] + }, + { + "cell_type": "markdown", + "id": "16f77320", + "metadata": {}, + "source": [ + "\n", + "## Introduction\n", + "\n", + "**Segregation** is a fundamental concept in social network analysis that measures how individuals with similar attributes tend to group together. While traditional segregation measures focus on pairwise relationships (edges), hypergraphs allow us to study segregation in **higher-order interactions** where multiple individuals interact simultaneously.\n", + "\n", + "This tutorial introduces **Random Walk Hypergraph Segregation (RWHS)**, a measure that uses random walks on hypergraphs to quantify segregation patterns. RWHS captures how likely it is for nodes with similar attributes to be encountered during random explorations of the hypergraph structure.\n", + "\n", + "**Key Reference:**\n", + "> Failla, A., Rossetti, G., & Cauteruccio, F. (2024). *Beyond Boundaries: Capturing Social Segregation on Hypernetworks*. International Conference on Advances in Social Networks Analysis and Mining, 40-55. Springer.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "a2e3986b", + "metadata": {}, + "source": [ + "\n", + "## What is Segregation in Hypergraphs?\n", + "\n", + "In a hypergraph, segregation captures whether nodes with similar attribute values (e.g., same gender, ethnicity, affiliation) tend to participate in the same hyperedges and their local neighborhoods.\n", + "\n", + "**Examples of Segregation in Hypergraphs:**\n", + "\n", + "- **Email groups**: Do people from the same department tend to be in the same group emails?\n", + "- **Scientific collaborations**: Do authors from the same institution collaborate more frequently?\n", + "- **Social gatherings**: Do people with similar interests attend the same events?\n", + "- **Online communities**: Do users with similar demographics participate in the same discussions?\n", + "\n", + "**High Segregation** means that nodes with similar attributes cluster together in the hypergraph structure. **Low Segregation** (high mixing) means that nodes with different attributes frequently interact.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "79fc7c08", + "metadata": {}, + "source": [ + "\n", + "## Random Walk Hypergraph Segregation (RWHS)\n", + "\n", + "RWHS measures segregation by performing random walks on the hypergraph and computing how often nodes with the same attribute values are encountered. The intuition is:\n", + "\n", + "- If a hypergraph is **highly segregated**, random walks starting from a node will frequently encounter nodes with the same attributes.\n", + "- If a hypergraph is **well-mixed**, random walks will encounter nodes with diverse attributes.\n", + "\n", + "RWHS returns a score for each node and each attribute, ranging from 0 to 1:\n", + "- **RWHS ≈ 1**: High segregation (the node mostly encounters similar nodes)\n", + "- **RWHS ≈ 0**: Low segregation (the node encounters diverse nodes)\n", + "\n", + "**Two Variants:**\n", + "\n", + "1. **Meet-wise RWHS**: Considers all nodes encountered in the walk\n", + "2. **Jump-wise RWHS**: Considers only consecutive pairs of nodes in the walk\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "14f8b4d9", + "metadata": {}, + "source": [ + "\n", + "### Meet-wise RWHS\n", + "\n", + "**Meet-wise RWHS** measures the proportion of nodes encountered in a random walk that share the same attribute value as the starting node.\n", + "\n", + "**Formula (intuitive):**\n", + "```\n", + "RWHS_meet(v, attr) = (# of visited nodes with same attr value as v) / (total # of visited nodes)\n", + "```\n", + "\n", + "**When to use:**\n", + "- You want to capture the **overall composition** of the neighborhood\n", + "- You care about **any encounter** during the walk, not just direct transitions\n", + "- Example: \"What fraction of people I meet in my social circles share my affiliation?\"\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "d50b6a88", + "metadata": {}, + "source": [ + "\n", + "### Jump-wise RWHS\n", + "\n", + "**Jump-wise RWHS** measures the proportion of consecutive transitions in a random walk where both nodes share the same attribute value.\n", + "\n", + "**Formula (intuitive):**\n", + "```\n", + "RWHS_jump(v, attr) = (# of consecutive pairs with same attr) / (total # of transitions)\n", + "```\n", + "\n", + "**When to use:**\n", + "- You want to capture **direct transitions** between similar nodes\n", + "- You care about **immediate connections**, not distant encounters\n", + "- Example: \"When I move from one group to another, how often do I stay within my affiliation?\"\n", + "\n", + "**Key Difference:**\n", + "- **Meet-wise** is more **global** (considers all nodes in the walk)\n", + "- **Jump-wise** is more **local** (considers only adjacent transitions)\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "59dcf032", + "metadata": {}, + "source": [ + "\n", + "## Static RWHS\n", + "\n", + "Let's start with the basic `rwhs()` function that operates on a single temporal snapshot." + ] + }, + { + "cell_type": "markdown", + "id": "7c9c515b", + "metadata": {}, + "source": [ + "\n", + "### Basic Example\n", + "\n", + "We'll create a small hypergraph with node attributes and compute RWHS scores." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d3251a77", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Created hypergraph with 8 nodes and 6 hyperedges\n", + "\n", + "Node groups:\n", + " Node 1: group A\n", + " Node 2: group A\n", + " Node 3: group A\n", + " Node 4: group B\n", + " Node 5: group B\n", + " Node 6: group B\n", + " Node 7: group C\n", + " Node 8: group C\n" + ] + } + ], + "source": [ + "from ash_model import ASH\n", + "from ash_model.measures.hyper_segregation import rwhs, temporal_rwhs\n", + "import random\n", + "import numpy as np\n", + "\n", + "# Set seed for reproducibility\n", + "random.seed(42)\n", + "np.random.seed(42)\n", + "\n", + "# Create a temporal hypergraph\n", + "h = ASH()\n", + "\n", + "# Add nodes with attributes (simulating a small community)\n", + "# Attribute: 'group' (A, B, or C)\n", + "node_attributes = {\n", + " 1: {'group': 'A'},\n", + " 2: {'group': 'A'},\n", + " 3: {'group': 'A'},\n", + " 4: {'group': 'B'},\n", + " 5: {'group': 'B'},\n", + " 6: {'group': 'B'},\n", + " 7: {'group': 'C'},\n", + " 8: {'group': 'C'},\n", + "}\n", + "\n", + "# Add nodes with their attributes\n", + "for node, attrs in node_attributes.items():\n", + " h.add_node(node, start=0, end=0, attr_dict=attrs)\n", + "\n", + "# Add hyperedges at time 0 with varying degrees of mixing\n", + "# High segregation: mostly within-group hyperedges\n", + "h.add_hyperedge([1, 2, 3], start=0, end=0) # All group A\n", + "h.add_hyperedge([4, 5, 6], start=0, end=0) # All group B\n", + "h.add_hyperedge([7, 8], start=0, end=0) # All group C\n", + "h.add_hyperedge([1, 2, 4], start=0, end=0) # Mixed A-B\n", + "h.add_hyperedge([5, 7], start=0, end=0) # Mixed B-C\n", + "h.add_hyperedge([3, 6, 8], start=0, end=0) # Mixed A-B-C\n", + "\n", + "print(f\"Created hypergraph with {h.number_of_nodes()} nodes and {h.number_of_hyperedges()} hyperedges\")\n", + "print(f\"\\nNode groups:\")\n", + "for node, attrs in node_attributes.items():\n", + " print(f\" Node {node}: group {attrs['group']}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "951afdd9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Meet-wise RWHS scores:\n", + "----------------------------------------\n", + "Node 1 (group A): RWHS = 0.427\n", + "Node 2 (group A): RWHS = 0.453\n", + "Node 3 (group A): RWHS = 0.385\n", + "Node 4 (group B): RWHS = 0.268\n", + "Node 5 (group B): RWHS = 0.367\n", + "Node 6 (group B): RWHS = 0.320\n", + "Node 7 (group C): RWHS = 0.207\n", + "Node 8 (group C): RWHS = 0.130\n", + "\n", + "📊 Interpretation:\n", + " Higher scores → Node encounters more nodes from its own group\n", + " Lower scores → Node encounters diverse groups\n" + ] + } + ], + "source": [ + "# Compute RWHS with meet-wise method\n", + "scores_meet = rwhs(h, s=1, tid=0, num_walks=100, walk_length=5, method=\"meet\")\n", + "\n", + "print(\"Meet-wise RWHS scores:\")\n", + "print(\"-\" * 40)\n", + "for node in sorted(scores_meet.keys()):\n", + " group = node_attributes[node]['group']\n", + " score = scores_meet[node]['group']\n", + " print(f\"Node {node} (group {group}): RWHS = {score:.3f}\")\n", + "\n", + "print(\"\\n📊 Interpretation:\")\n", + "print(\" Higher scores → Node encounters more nodes from its own group\")\n", + "print(\" Lower scores → Node encounters diverse groups\")" + ] + }, + { + "cell_type": "markdown", + "id": "c9013c70", + "metadata": {}, + "source": [ + "\n", + "### Comparing Methods\n", + "\n", + "Let's compare meet-wise and jump-wise RWHS to understand the difference." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "32473188", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Comparison: Meet-wise vs Jump-wise RWHS\n", + "============================================================\n", + "Node Group Meet-wise Jump-wise Difference \n", + "------------------------------------------------------------\n", + "1 A 0.435 0.625 -0.190\n", + "2 A 0.403 0.625 -0.222\n", + "3 A 0.362 0.568 -0.205\n", + "4 B 0.285 0.552 -0.268\n", + "5 B 0.372 0.585 -0.212\n", + "6 B 0.352 0.522 -0.170\n", + "7 C 0.230 0.492 -0.262\n", + "8 C 0.145 0.415 -0.270\n", + "\n", + "📊 Observations:\n", + " • Meet-wise considers all encounters → captures global mixing\n", + " • Jump-wise considers only transitions → captures local mixing\n", + " • Differences reveal whether segregation is global vs local\n" + ] + } + ], + "source": [ + "# Compute both methods\n", + "scores_meet = rwhs(h, s=1, tid=0, num_walks=100, walk_length=5, method=\"meet\")\n", + "scores_jump = rwhs(h, s=1, tid=0, num_walks=100, walk_length=5, method=\"jump\")\n", + "\n", + "print(\"Comparison: Meet-wise vs Jump-wise RWHS\")\n", + "print(\"=\" * 60)\n", + "print(f\"{'Node':<6} {'Group':<7} {'Meet-wise':<12} {'Jump-wise':<12} {'Difference':<12}\")\n", + "print(\"-\" * 60)\n", + "\n", + "for node in sorted(scores_meet.keys()):\n", + " group = node_attributes[node]['group']\n", + " meet_score = scores_meet[node]['group']\n", + " jump_score = scores_jump[node]['group']\n", + " diff = meet_score - jump_score\n", + " \n", + " print(f\"{node:<6} {group:<7} {meet_score:<12.3f} {jump_score:<12.3f} {diff:+.3f}\")\n", + "\n", + "print(\"\\n📊 Observations:\")\n", + "print(\" • Meet-wise considers all encounters → captures global mixing\")\n", + "print(\" • Jump-wise considers only transitions → captures local mixing\")\n", + "print(\" • Differences reveal whether segregation is global vs local\")" + ] + }, + { + "cell_type": "markdown", + "id": "8a901727", + "metadata": {}, + "source": [ + "\n", + "### Effect of Random Walk Parameters\n", + "\n", + "The RWHS measure depends on random walk parameters `p` (return parameter) and `q` (in-out parameter). Let's explore their effect.\n", + "\n", + "**Parameters:**\n", + "- **p**: Controls the likelihood of returning to the previous node\n", + " - High p → less likely to return (more exploration)\n", + " - Low p → more likely to return (more local)\n", + "- **q**: Controls the likelihood of exploring vs. staying local\n", + " - High q → prefer nodes close to previous position\n", + " - Low q → prefer exploring distant nodes\n", + "\n", + "These parameters come from Node2Vec random walks." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "6b2f574d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Effect of Random Walk Parameters on RWHS\n", + "======================================================================\n", + "\n", + "Balanced (BFS-DFS) (p=1.0, q=1.0):\n", + " Average RWHS: 0.308\n", + " Node 1 (group A): 0.412\n", + " Node 4 (group B): 0.300\n", + " Node 7 (group C): 0.220\n", + "\n", + "More local (high q) (p=0.5, q=2.0):\n", + " Average RWHS: 0.308\n", + " Node 1 (group A): 0.405\n", + " Node 4 (group B): 0.320\n", + " Node 7 (group C): 0.212\n", + "\n", + "More exploratory (low q) (p=2.0, q=0.5):\n", + " Average RWHS: 0.333\n", + " Node 1 (group A): 0.448\n", + " Node 4 (group B): 0.320\n", + " Node 7 (group C): 0.210\n", + "\n", + "📊 Interpretation:\n", + " • Different parameters capture different notions of neighborhood\n", + " • Choose parameters based on the mixing scale you want to measure\n" + ] + } + ], + "source": [ + "# Test different parameter combinations\n", + "param_configs = [\n", + " (1.0, 1.0, \"Balanced (BFS-DFS)\"),\n", + " (0.5, 2.0, \"More local (high q)\"),\n", + " (2.0, 0.5, \"More exploratory (low q)\"),\n", + "]\n", + "\n", + "print(\"Effect of Random Walk Parameters on RWHS\")\n", + "print(\"=\" * 70)\n", + "\n", + "for p, q, description in param_configs:\n", + " scores = rwhs(h, s=1, tid=0, num_walks=100, walk_length=5, p=p, q=q, method=\"meet\")\n", + " \n", + " avg_score = np.mean([scores[node]['group'] for node in scores])\n", + " \n", + " print(f\"\\n{description} (p={p}, q={q}):\")\n", + " print(f\" Average RWHS: {avg_score:.3f}\")\n", + " \n", + " # Show a few node scores\n", + " sample_nodes = [1, 4, 7] # One from each group\n", + " for node in sample_nodes:\n", + " group = node_attributes[node]['group']\n", + " score = scores[node]['group']\n", + " print(f\" Node {node} (group {group}): {score:.3f}\")\n", + "\n", + "print(\"\\n📊 Interpretation:\")\n", + "print(\" • Different parameters capture different notions of neighborhood\")\n", + "print(\" • Choose parameters based on the mixing scale you want to measure\")" + ] + }, + { + "cell_type": "markdown", + "id": "40761b30", + "metadata": {}, + "source": [ + "\n", + "## Temporal RWHS\n", + "\n", + "For temporal hypergraphs, we can use **time-respecting random walks** that respect the temporal ordering of hyperedges. This is useful for analyzing segregation in dynamic networks where interactions have a temporal structure.\n", + "\n", + "**Temporal RWHS** uses `temporal_rwhs()` which:\n", + "- Performs random walks on hyperedges (not nodes)\n", + "- Respects temporal constraints (can only move forward in time)\n", + "- Captures segregation in the temporal evolution" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "aa9ac44d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Temporal hypergraph created\n", + " Snapshots: [0, 1]\n", + " Nodes: 8\n", + " Hyperedges: 6\n" + ] + } + ], + "source": [ + "# Create a temporal hypergraph with evolution\n", + "h_temp = ASH()\n", + "\n", + "# Add nodes with attributes across both time periods\n", + "for node, attrs in node_attributes.items():\n", + " h_temp.add_node(node, start=0, end=1, attr_dict=attrs)\n", + "\n", + "# Time 0: Initial configuration (mixed)\n", + "h_temp.add_hyperedge([1, 2, 4], eid=\"e1\", start=0, end=0)\n", + "h_temp.add_hyperedge([3, 5], eid=\"e2\", start=0, end=0)\n", + "h_temp.add_hyperedge([6, 7, 8], eid=\"e3\", start=0, end=0)\n", + "\n", + "# Time 1: More segregated\n", + "h_temp.add_hyperedge([1, 2, 3], eid=\"e4\", start=1, end=1) # Group A\n", + "h_temp.add_hyperedge([4, 5, 6], eid=\"e5\", start=1, end=1) # Group B\n", + "h_temp.add_hyperedge([7, 8], eid=\"e6\", start=1, end=1) # Group C\n", + "\n", + "print(\"Temporal hypergraph created\")\n", + "print(f\" Snapshots: {h_temp.temporal_snapshots_ids()}\")\n", + "print(f\" Nodes: {h_temp.number_of_nodes()}\")\n", + "print(f\" Hyperedges: {h_temp.number_of_hyperedges()}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "cb5732fd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Computing Temporal RWHS (this uses time-respecting random walks)...\n", + "\n", + "Temporal RWHS scores:\n", + "----------------------------------------\n", + "\n", + "📊 Interpretation:\n", + " Temporal RWHS captures segregation along temporal paths\n", + " Useful for understanding how groups interact over time\n" + ] + } + ], + "source": [ + "# Compute temporal RWHS\n", + "# Note: temporal_rwhs works on hyperedge walks\n", + "print(\"Computing Temporal RWHS (this uses time-respecting random walks)...\")\n", + "\n", + "scores_temporal = temporal_rwhs(\n", + " h_temp, \n", + " s=1, \n", + " tid=0, # Starting from time 0\n", + " num_walks=50, \n", + " walk_length=3,\n", + " method=\"meet\"\n", + ")\n", + "\n", + "print(\"\\nTemporal RWHS scores:\")\n", + "print(\"-\" * 40)\n", + "for node in sorted(scores_temporal.keys()):\n", + " if node in node_attributes:\n", + " group = node_attributes[node]['group']\n", + " score = scores_temporal[node]['group']\n", + " print(f\"Node {node} (group {group}): RWHS = {score:.3f}\")\n", + "\n", + "print(\"\\n📊 Interpretation:\")\n", + "print(\" Temporal RWHS captures segregation along temporal paths\")\n", + "print(\" Useful for understanding how groups interact over time\")" + ] + }, + { + "cell_type": "markdown", + "id": "45975238", + "metadata": {}, + "source": [ + "\n", + "## Practical Examples\n", + "\n", + "Let's explore some practical scenarios where RWHS is useful." + ] + }, + { + "cell_type": "markdown", + "id": "38cf4b61", + "metadata": {}, + "source": [ + "\n", + "### Example 1: Measuring Attribute Mixing\n", + "\n", + "Create a hypergraph and measure mixing for multiple attributes." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "11299e47", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Created hypergraph with 20 nodes and 28 hyperedges\n", + "\n", + "Node attributes:\n", + " Departments: Engineering (1-10), Marketing (11-20)\n", + " Seniority: Junior (every 3rd node), Senior (others)\n" + ] + } + ], + "source": [ + "# Create a larger hypergraph with multiple attributes\n", + "h_multi = ASH()\n", + "\n", + "# 20 nodes with two attributes: department and seniority\n", + "for i in range(1, 21):\n", + " dept = 'Engineering' if i <= 10 else 'Marketing'\n", + " seniority = 'Junior' if i % 3 == 0 else 'Senior'\n", + " h_multi.add_node(i, start=0, end=0, attr_dict={'department': dept, 'seniority': seniority})\n", + "\n", + "# Add hyperedges with some department mixing\n", + "np.random.seed(42)\n", + "for j in range(30):\n", + " # Mix of within-department and cross-department hyperedges\n", + " if np.random.random() < 0.7: # 70% within department\n", + " dept_idx = np.random.choice([0, 1])\n", + " start_node = 1 + dept_idx * 10\n", + " size = np.random.randint(2, 5)\n", + " nodes = np.random.choice(range(start_node, start_node + 10), size=size, replace=False)\n", + " else: # 30% mixed\n", + " size = np.random.randint(2, 5)\n", + " nodes = np.random.choice(range(1, 21), size=size, replace=False)\n", + " \n", + " h_multi.add_hyperedge(list(nodes), eid=f\"e{j+1}\", start=0, end=0)\n", + "\n", + "print(f\"Created hypergraph with {h_multi.number_of_nodes()} nodes and {h_multi.number_of_hyperedges()} hyperedges\")\n", + "print(f\"\\nNode attributes:\")\n", + "print(f\" Departments: Engineering (1-10), Marketing (11-20)\")\n", + "print(f\" Seniority: Junior (every 3rd node), Senior (others)\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "8940f25e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Segregation Analysis by Attribute\n", + "============================================================\n", + "\n", + "DEPARTMENT:\n", + " Average RWHS: 0.781 ± 0.069\n", + " Min: 0.577\n", + " Max: 0.869\n", + " → HIGH segregation\n", + "\n", + "SENIORITY:\n", + " Average RWHS: 0.483 ± 0.172\n", + " Min: 0.176\n", + " Max: 0.666\n", + " → LOW segregation (well-mixed)\n", + "\n", + "📊 Interpretation:\n", + " Compare RWHS across attributes to identify which dimensions\n", + " show stronger segregation patterns\n" + ] + } + ], + "source": [ + "# Compute RWHS for both attributes\n", + "scores_multi = rwhs(h_multi, s=1, tid=0, num_walks=200, walk_length=8, method=\"meet\")\n", + "\n", + "# Analyze segregation by attribute\n", + "print(\"Segregation Analysis by Attribute\")\n", + "print(\"=\" * 60)\n", + "\n", + "for attr in ['department', 'seniority']:\n", + " scores_for_attr = [scores_multi[node][attr] for node in scores_multi if attr in scores_multi[node]]\n", + " \n", + " if scores_for_attr:\n", + " avg_score = np.mean(scores_for_attr)\n", + " std_score = np.std(scores_for_attr)\n", + " \n", + " print(f\"\\n{attr.upper()}:\")\n", + " print(f\" Average RWHS: {avg_score:.3f} ± {std_score:.3f}\")\n", + " print(f\" Min: {min(scores_for_attr):.3f}\")\n", + " print(f\" Max: {max(scores_for_attr):.3f}\")\n", + " \n", + " # Classify segregation level\n", + " if avg_score > 0.7:\n", + " level = \"HIGH segregation\"\n", + " elif avg_score > 0.5:\n", + " level = \"MODERATE segregation\"\n", + " else:\n", + " level = \"LOW segregation (well-mixed)\"\n", + " print(f\" → {level}\")\n", + "\n", + "print(\"\\n📊 Interpretation:\")\n", + "print(\" Compare RWHS across attributes to identify which dimensions\")\n", + "print(\" show stronger segregation patterns\")" + ] + }, + { + "cell_type": "markdown", + "id": "0417d76d", + "metadata": {}, + "source": [ + "\n", + "### Example 2: Comparing Segregation Across Time\n", + "\n", + "Track how segregation evolves over time." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "2dc48b86", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Created temporal hypergraph with evolving segregation\n", + " Snapshots: [0, 1, 2]\n" + ] + } + ], + "source": [ + "# Create a hypergraph that evolves from mixed to segregated\n", + "h_evolution = ASH()\n", + "\n", + "# Add nodes with attributes across all time periods\n", + "for i in range(1, 13):\n", + " group = 'A' if i <= 4 else ('B' if i <= 8 else 'C')\n", + " h_evolution.add_node(i, start=0, end=2, attr_dict={'group': group})\n", + "\n", + "# Time 0: Well-mixed (low segregation)\n", + "mixed_edges = [\n", + " [1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12], # Mixed groups\n", + " [1, 2, 5], [3, 6, 9], [4, 7, 10] # More mixing\n", + "]\n", + "for idx, nodes in enumerate(mixed_edges):\n", + " h_evolution.add_hyperedge(nodes, eid=f\"t0_e{idx+1}\", start=0, end=0)\n", + "\n", + "# Time 1: Moderate segregation\n", + "moderate_edges = [\n", + " [1, 2, 3], [5, 6, 7], [9, 10, 11], # Within-group\n", + " [1, 5], [4, 8], [7, 11] # Some mixing\n", + "]\n", + "for idx, nodes in enumerate(moderate_edges):\n", + " h_evolution.add_hyperedge(nodes, eid=f\"t1_e{idx+1}\", start=1, end=1)\n", + "\n", + "# Time 2: High segregation\n", + "segregated_edges = [\n", + " [1, 2, 3, 4], # All A\n", + " [5, 6, 7, 8], # All B\n", + " [9, 10, 11, 12], # All C\n", + "]\n", + "for idx, nodes in enumerate(segregated_edges):\n", + " h_evolution.add_hyperedge(nodes, eid=f\"t2_e{idx+1}\", start=2, end=2)\n", + "\n", + "print(\"Created temporal hypergraph with evolving segregation\")\n", + "print(f\" Snapshots: {h_evolution.temporal_snapshots_ids()}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "01a28ead", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Segregation Evolution Over Time\n", + "============================================================\n", + "\n", + "Time 0:\n", + " Average RWHS: 0.162\n", + " Nodes with RWHS > 0.5: 0/12\n", + " Node 1: 0.268\n", + " Node 5: 0.116\n", + " Node 9: 0.096\n", + "\n", + "Time 1:\n", + " Average RWHS: 0.508\n", + " Nodes with RWHS > 0.5: 5/9\n", + " Node 1: 0.408\n", + " Node 5: 0.408\n", + " Node 9: 0.596\n", + "\n", + "Time 2:\n", + " Average RWHS: 0.789\n", + " Nodes with RWHS > 0.5: 12/12\n", + " Node 1: 0.768\n", + " Node 5: 0.794\n", + " Node 9: 0.798\n", + "\n", + "📊 Trend Analysis:\n", + " t0 → t1: RWHS ↑ increased by 0.346\n", + " t1 → t2: RWHS ↑ increased by 0.281\n", + "\n", + " → The hypergraph became more segregated over time\n" + ] + } + ], + "source": [ + "# Compute RWHS at each time point\n", + "print(\"Segregation Evolution Over Time\")\n", + "print(\"=\" * 60)\n", + "\n", + "time_scores = []\n", + "for t in range(3):\n", + " scores_t = rwhs(h_evolution, s=1, tid=t, num_walks=100, walk_length=6, method=\"meet\")\n", + " \n", + " # Compute average RWHS\n", + " group_scores = [scores_t[node]['group'] for node in scores_t if 'group' in scores_t[node]]\n", + " avg_score = np.mean(group_scores) if group_scores else 0\n", + " time_scores.append(avg_score)\n", + " \n", + " print(f\"\\nTime {t}:\")\n", + " print(f\" Average RWHS: {avg_score:.3f}\")\n", + " print(f\" Nodes with RWHS > 0.5: {sum(1 for s in group_scores if s > 0.5)}/{len(group_scores)}\")\n", + " \n", + " # Sample nodes\n", + " sample_nodes = [1, 5, 9] # One from each group\n", + " for node in sample_nodes:\n", + " if node in scores_t:\n", + " score = scores_t[node]['group']\n", + " print(f\" Node {node}: {score:.3f}\")\n", + "\n", + "print(\"\\n📊 Trend Analysis:\")\n", + "for i in range(1, len(time_scores)):\n", + " change = time_scores[i] - time_scores[i-1]\n", + " direction = \"↑ increased\" if change > 0 else \"↓ decreased\"\n", + " print(f\" t{i-1} → t{i}: RWHS {direction} by {abs(change):.3f}\")\n", + "\n", + "print(\"\\n → The hypergraph became more segregated over time\")" + ] + }, + { + "cell_type": "markdown", + "id": "053cd0aa", + "metadata": {}, + "source": [ + "\n", + "### Example 3: Parameter Tuning\n", + "\n", + "Understanding how walk length and number of walks affect RWHS." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f2784850", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Temporal hypergraph created\n", + " Snapshots: [0, 1]\n", + " Nodes: 8\n", + " Hyperedges: 6\n" + ] + } + ], + "source": [ + "# Create a temporal hypergraph with evolution\n", + "h_temp = ASH()\n", + "\n", + "# Add nodes with attributes across both time periods\n", + "for node, attrs in node_attributes.items():\n", + " h_temp.add_node(node, start=0, end=1, attr_dict=attrs)\n", + "\n", + "# Time 0: Initial configuration (mixed)\n", + "h_temp.add_hyperedge([1, 2, 4], eid=\"e1\", start=0, end=0)\n", + "h_temp.add_hyperedge([3, 5], eid=\"e2\", start=0, end=0)\n", + "h_temp.add_hyperedge([6, 7, 8], eid=\"e3\", start=0, end=0)\n", + "\n", + "# Time 1: More segregated\n", + "h_temp.add_hyperedge([1, 2, 3], eid=\"e4\", start=1, end=1) # Group A\n", + "h_temp.add_hyperedge([4, 5, 6], eid=\"e5\", start=1, end=1) # Group B\n", + "h_temp.add_hyperedge([7, 8], eid=\"e6\", start=1, end=1) # Group C\n", + "\n", + "print(\"Temporal hypergraph created\")\n", + "print(f\" Snapshots: {h_temp.temporal_snapshots_ids()}\")\n", + "print(f\" Nodes: {h_temp.number_of_nodes()}\")\n", + "print(f\" Hyperedges: {h_temp.number_of_hyperedges()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "913ebe65", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "Random Walk Hypergraph Segregation (RWHS) provides a powerful framework for measuring segregation in higher-order interactions.\n", + "\n", + "**Key Takeaways:**\n", + "\n", + "1. **Two Methods:**\n", + " - **Meet-wise**: Global mixing (considers all encounters)\n", + " - **Jump-wise**: Local mixing (considers consecutive transitions)\n", + "\n", + "2. **Parameters:**\n", + " - **num_walks**: More walks → more stable estimates\n", + " - **walk_length**: Longer walks → broader neighborhoods\n", + " - **p, q**: Control exploration vs. exploitation (from Node2Vec)\n", + " - **s**: Minimum overlap for hyperedge connections\n", + "\n", + "3. **Temporal Analysis:**\n", + " - Use `temporal_rwhs()` for time-respecting random walks\n", + " - Track segregation evolution over time\n", + " - Compare segregation across different temporal windows\n", + "\n", + "4. **Applications:**\n", + " - Measure mixing across multiple attributes\n", + " - Compare segregation levels between groups\n", + " - Identify temporal trends in segregation\n", + " - Evaluate interventions designed to promote diversity\n", + "\n", + "**When to Use RWHS:**\n", + "- ✅ Analyzing group interactions in collaborative networks\n", + "- ✅ Measuring diversity in team formations\n", + "- ✅ Studying temporal evolution of mixing patterns\n", + "- ✅ Comparing segregation across different attributes\n", + "\n", + "**Next Steps:**\n", + "- Explore the [walks tutorial](02-walks.ipynb) for understanding random walks\n", + "- Check the [attribute analysis tutorial](01-attribute_analysis.ipynb) for other attribute-based measures\n", + "- See the [multiego tutorial](05-multiego.ipynb) for group-centric analysis\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "markdown", + "id": "a8552f6f", + "metadata": {}, + "source": [ + "\n", + "## References\n", + "\n", + "**Main Reference:**\n", + "- Failla, A., Rossetti, G., & Cauteruccio, F. (2024). *Beyond Boundaries: Capturing Social Segregation on Hypernetworks*. In International Conference on Advances in Social Networks Analysis and Mining (pp. 40-55). Springer.\n", + "\n", + "**Related Work:**\n", + "- Node2Vec random walks: Grover, A., & Leskovec, J. (2016). *node2vec: Scalable feature learning for networks*. KDD.\n", + "- Hypergraph theory: Berge, C. (1984). *Hypergraphs: combinatorics of finite sets*. North-Holland.\n", + "\n", + "[🔝 To top](#table-of-contents)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8fd79ae6", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}