Add nominate_cycle_breakers method

Author: seddonym

CHANGELOG.rst

@@ -2,6 +2,11 @@
 Changelog
 =========
 
+latest
+------
+
+* Add `nominate_cycle_breakers` method.
+
 3.12 (2025-10-09)
 -----------------
 

docs/usage.rst

@@ -198,7 +198,7 @@ Methods for analysing direct imports
 
     Find all direct imports matching the passed import expression.
 
-    The imports are returned are in the following form::
+    The imports returned are in the following form::
 
         [
             {
@@ -505,6 +505,40 @@ Higher level analysis
 
         ``frozenset[str]``:  Imported modules at the end of the chain.
 
+.. py:function:: ImportGraph.nominate_cycle_breakers(package)
+
+    Choose an approximately minimal set of dependencies that, if removed, would make the package locally acyclic.
+
+    - 'Acyclic' means that there are no direct dependency cycles between the package's children. Indirect
+      dependencies (i.e. ones involving modules outside the supplied package) are disregarded,
+      as are imports between the package and its children.
+    - 'Dependency cycles' mean cycles between the *squashed* children (see `Terminology`_ above).
+
+    Multiple sets of cycle breakers can exist for a given package. To arrive at this particular set, the following
+    approach is used:
+
+    1. Create a graph whose nodes are each child of the package.
+    2. For each pair of children, add directed edges corresponding to whether there are imports between those two
+       children (as packages, rather than individual modules). The edges are weighted according to the number of
+       _dependencies_ they represent: this is usually the same as the number of imports, but if a module imports
+       another module in multiple places, it will be treated as a single dependency.
+    3. Calculate the approximately
+       `minimum weighted feedback arc set <https://en.wikipedia.org/wiki/Feedback_arc_set>`_.
+       This attempts to find a set of edges with the smallest total weight that can be removed from the graph in order
+       to make it acyclic. It uses the greedy cycle-breaking heuristic of Eades, Lin and Smyth: not guaranteed
+       to find the optimal solution, but it is faster than alternatives.
+    4. These edges are then used to look up all the concrete imports in the fully unsquashed graph, which are returned.
+       For example, an edge discovered in step 3. of ``mypackage.foo -> mypackage.bar``, with a weight 3, might correspond
+       to these three imports: ``mypackage.foo.blue -> mypackage.bar.green``,
+       ``mypackage.foo.blue.one -> mypackage.bar.green.two``, and ``mypackage.foo.blue -> mypackage.bar.green.three``.
+
+    :param str package: The package in the graph to check for cycles. If a module with no children is passed,
+      an empty set is be returned.
+    :return: A set of imports that, if removed, would make the imports between the the children of the supplied
+      package acyclic.
+    :rtype: ``set[tuple[str, str]]``. In each import tuple, the first element is the importer module and the second
+      is the imported.
+
 Methods for manipulating the graph
 ----------------------------------
 

pyproject.toml

@@ -16,6 +16,7 @@ authors = [
 ]
 requires-python = ">=3.9"
 dependencies = [
+    "igraph>=0.11.9",
     "typing-extensions>=3.10.0.0",
 ]
 classifiers = [

src/grimp/application/graph.py

@@ -1,8 +1,9 @@
 from __future__ import annotations
+import itertools
 from typing import List, Optional, Sequence, Set, Tuple, TypedDict
 from grimp.domain.analysis import PackageDependency, Route
 from grimp.domain.valueobjects import Layer
-
+import igraph as ig  # type: ignore
 from grimp import _rustgrimp as rust  # type: ignore[attr-defined]
 from grimp.exceptions import (
     ModuleNotPresent,
@@ -17,6 +18,11 @@ class Import(TypedDict):
     imported: str
 
 
+# Corresponds to importer, imported.
+# Prefer this form to Import, as it's both more lightweight, and hashable.
+ImportTuple = Tuple[str, str]
+
+
 class DetailedImport(Import):
     line_number: int
     line_contents: str
@@ -440,6 +446,57 @@ def find_illegal_dependencies_for_layers(
 
         return _dependencies_from_tuple(result)
 
+    def nominate_cycle_breakers(self, package: str) -> set[ImportTuple]:
+        """
+        Identify a set of imports that, if removed, would make the package locally acyclic.
+        """
+        children = self.find_children(package)
+        if len(children) < 2:
+            return set()
+        igraph = ig.Graph(directed=True)
+        igraph.add_vertices([package, *children])
+        edges: list[tuple[str, str]] = []
+        weights: list[int] = []
+        for downstream, upstream in itertools.permutations(children, r=2):
+            total_imports = 0
+            for expression in (
+                f"{downstream} -> {upstream}",
+                f"{downstream}.** -> {upstream}",
+                f"{downstream} -> {upstream}.**",
+                f"{downstream}.** -> {upstream}.**",
+            ):
+                total_imports += len(self.find_matching_direct_imports(expression))
+            if total_imports:
+                edges.append((downstream, upstream))
+                weights.append(total_imports)
+
+        igraph.add_edges(edges)
+        igraph.es["weight"] = weights
+
+        arc_set = igraph.feedback_arc_set(weights="weight")
+
+        squashed_imports: list[Import] = []
+        for edge_id in arc_set:
+            edge = igraph.es[edge_id]
+            squashed_imports.append(
+                {
+                    "importer": edge.source_vertex["name"],
+                    "imported": edge.target_vertex["name"],
+                }
+            )
+
+        unsquashed_imports: list[Import] = []
+        for squashed_import in squashed_imports:
+            for pattern in (
+                f"{squashed_import['importer']} -> {squashed_import['imported']}",
+                f"{squashed_import['importer']}.** -> {squashed_import['imported']}",
+                f"{squashed_import['importer']} -> {squashed_import['imported']}.**",
+                f"{squashed_import['importer']}.** -> {squashed_import['imported']}.**",
+            ):
+                unsquashed_imports.extend(self.find_matching_direct_imports(pattern))
+
+        return {(i["importer"], i["imported"]) for i in unsquashed_imports}
+
     # Dunder methods
     # --------------
 

tests/unit/application/graph/test_cycle_breakers.py

@@ -0,0 +1,179 @@
+from grimp.application.graph import ImportGraph
+import pytest
+
+
+class TestFindCycleBreakers:
+    def test_empty_graph(self):
+        graph = ImportGraph()
+        graph.add_module("pkg")
+
+        result = graph.nominate_cycle_breakers("pkg")
+
+        assert result == set()
+
+    @pytest.mark.parametrize(
+        "module",
+        (
+            "pkg",
+            "pkg.foo",
+            "pkg.foo.blue",
+        ),
+    )
+    def test_graph_with_no_imports(self, module: str):
+        graph = self._build_graph_with_no_imports()
+
+        result = graph.nominate_cycle_breakers(module)
+
+        assert result == set()
+
+    @pytest.mark.parametrize(
+        "module",
+        (
+            "pkg",
+            "pkg.bar",
+            "pkg.foo.blue",
+            "pkg.foo.green",  # Leaf package.
+        ),
+    )
+    def test_acyclic_graph(self, module: str):
+        graph = self._build_acyclic_graph()
+
+        result = graph.nominate_cycle_breakers(module)
+
+        assert result == set()
+
+    def test_one_breaker(self):
+        graph = self._build_acyclic_graph()
+        importer, imported = "pkg.bar.red.four", "pkg.foo.blue.two"
+        graph.add_import(importer=importer, imported=imported)
+        result = graph.nominate_cycle_breakers("pkg")
+
+        assert result == {(importer, imported)}
+
+    def test_three_breakers(self):
+        graph = self._build_acyclic_graph()
+        imports = {
+            ("pkg.bar.red.four", "pkg.foo.blue.two"),
+            ("pkg.bar.yellow", "pkg.foo.blue.three"),
+            ("pkg.bar", "pkg.foo.blue.three"),
+        }
+        for importer, imported in imports:
+            graph.add_import(importer=importer, imported=imported)
+
+        result = graph.nominate_cycle_breakers("pkg")
+
+        assert result == imports
+
+    def test_nominated_based_on_dependencies_rather_than_imports(self):
+        graph = self._build_acyclic_graph()
+        # Add lots of imports from a single module - this will be treated as
+        # a single dependency.
+        importer, imported = "pkg.bar.red.four", "pkg.foo.blue.two"
+        for i in range(1, 30):
+            graph.add_import(
+                importer=importer, imported=imported, line_number=i, line_contents="-"
+            )
+
+        graph.add_import(importer=importer, imported=imported)
+
+        result = graph.nominate_cycle_breakers("pkg")
+
+        assert result == {(importer, imported)}
+
+    def test_imports_between_passed_package_and_children_are_disregarded(self):
+        graph = self._build_acyclic_graph()
+        parent, child = "pkg.foo.blue", "pkg.foo"
+        graph.add_import(importer=parent, imported=child)
+        graph.add_import(importer=child, imported=parent)
+
+        result = graph.nominate_cycle_breakers(parent)
+
+        assert result == set()
+
+    def test_on_child_of_root(self):
+        graph = self._build_acyclic_graph()
+        imports = {
+            ("pkg.bar.red.five", "pkg.bar.yellow.eight"),
+            ("pkg.bar.red", "pkg.bar.yellow"),
+        }
+        for importer, imported in imports:
+            graph.add_import(importer=importer, imported=imported)
+
+        result = graph.nominate_cycle_breakers("pkg.bar")
+
+        assert result == imports
+
+    def test_on_grandchild_of_root(self):
+        graph = self._build_acyclic_graph()
+        imports = {
+            ("pkg.bar.orange.ten.gamma", "pkg.bar.orange.nine.alpha"),
+            ("pkg.bar.orange.ten", "pkg.bar.orange.nine.alpha"),
+        }
+        for importer, imported in imports:
+            graph.add_import(importer=importer, imported=imported)
+
+        result = graph.nominate_cycle_breakers("pkg.bar.orange")
+
+        assert result == imports
+
+    def test_on_package_with_one_child(self):
+        graph = self._build_acyclic_graph()
+        graph.add_module("pkg.bar.orange.ten.gamma.onechild")
+
+        result = graph.nominate_cycle_breakers("pkg.bar.orange.ten.gamma")
+
+        assert result == set()
+
+    def _build_graph_with_no_imports(self) -> ImportGraph:
+        graph = ImportGraph()
+        for module in (
+            "pkg",
+            "pkg.foo",
+            "pkg.foo.blue",
+            "pkg.foo.blue.one",
+            "pkg.foo.blue.two",
+            "pkg.foo.green",
+            "pkg.bar",
+            "pkg.bar.red",
+            "pkg.bar.red.three",
+            "pkg.bar.red.four",
+            "pkg.bar.red.five",
+            "pkg.bar.red.six",
+            "pkg.bar.red.seven",
+            "pkg.bar.yellow",
+            "pkg.bar.yellow.eight",
+            "pkg.bar.orange",
+            "pkg.bar.orange.nine",
+            "pkg.bar.orange.nine.alpha",
+            "pkg.bar.orange.nine.beta",
+            "pkg.bar.orange.ten",
+            "pkg.bar.orange.ten.gamma",
+            "pkg.bar.orange.ten.delta",
+        ):
+            graph.add_module(module)
+        return graph
+
+    def _build_acyclic_graph(self) -> ImportGraph:
+        graph = self._build_graph_with_no_imports()
+        # Add imports that make:
+        #   pkg.foo -> pkg.bar
+        #   pkg.bar.yellow -> pkg.foo.red
+        #   pkg.bar.orange.nine -> pkg.bar.orange.ten
+        for importer, imported in (
+            ("pkg.foo", "pkg.bar.red"),
+            ("pkg.foo.green", "pkg.bar.yellow"),
+            ("pkg.foo.blue.two", "pkg.bar.red.three"),
+            ("pkg.foo.blue.two", "pkg.bar.red.four"),
+            ("pkg.foo.blue.two", "pkg.bar.red.five"),
+            ("pkg.foo.blue.two", "pkg.bar.red.six"),
+            ("pkg.foo.blue.two", "pkg.bar.red.seven"),
+            ("pkg.bar.yellow", "pkg.bar.red"),
+            ("pkg.bar.yellow.eight", "pkg.bar.red.three"),
+            ("pkg.bar.yellow.eight", "pkg.bar.red.four"),
+            ("pkg.bar.yellow.eight", "pkg.bar.red.five"),
+            ("pkg.bar.orange.nine", "pkg.bar.orange.ten.gamma"),
+            ("pkg.bar.orange.nine.alpha", "pkg.bar.orange.ten.gamma"),
+            ("pkg.bar.orange.nine.beta", "pkg.bar.orange.ten.delta"),
+        ):
+            graph.add_import(importer=importer, imported=imported)
+        return graph