This repository investigates how local transition events accumulate into global connectivity structures in dynamically evolving networks.
It is part of a broader research program on complex systems, agent-based modeling, and emergent connectivity developed under the Meccanismo Complesso initiative.
Many complex systems can be represented as collections of local states connected by observed transitions.
Examples include:
- diffusion processes
- exploration dynamics
- adaptive landscapes
- organizational search
- metastable systems
This repository studies a minimal mechanism:
local transitions → transition accumulation → giant connected component
The goal is not to reproduce classical static percolation models, but to investigate a percolation-like emergence of connectivity in dynamically generated transition networks.
In particular, the project explores how heterogeneous mobility progressively transforms fragmented transition structures into globally connected networks.
Global connectivity does not necessarily require optimization, planning, or centralized coordination.
Instead, large-scale connectivity can emerge from the accumulation of simple local transitions generated by heterogeneous movement dynamics.
Agents move across a discrete state space composed of multiple possible states.
Two movement regimes are considered:
- Mostly local transitions
- Strong persistence in nearby states
- Low-mobility behavior
- Larger stochastic jumps
- Increased state-space coverage
- Higher transition variability
Each observed transition creates a directed edge in a transition graph.
As transitions accumulate over time, the graph progressively expands and reorganizes.
| Parameter | Value |
|---|---|
| Number of agents | 80 |
| Number of states | 120 |
| Simulation steps | 120 |
| Exploratory fraction | 0.00 – 0.10 |
| Network type | Directed transition graph |
The generated transition graph is analyzed using standard network observables:
- Graph density
- Mean degree
- Giant weak component ratio
transition-networks/
│
├── README.md
├── requirements.txt
│
├── src/
│ ├── simulation.py
│ ├── graph_builder.py
│ └── metrics.py
│
├── scripts/
│ ├── run_simulation.py
│ └── analyze_network.py
│
└── figures/
pip install -r requirements.txtpython scripts/run_simulation.py
python scripts/analyze_network.py
At low exploratory fractions, the transition graph remains fragmented.
As exploratory transitions increase, disconnected regions progressively merge into a large connected structure.
This suggests that global connectivity can emerge from the accumulation of local transition events without requiring adaptive strategies or optimization.
The transition graph progressively reorganizes as the exploratory fraction increases.
At low exploratory fractions, the graph remains fragmented into multiple disconnected components.
As exploratory mobility increases, previously isolated regions become connected through accumulated transition events, eventually generating a giant connected structure.
Blue nodes represent the giant weak component, while gray nodes correspond to smaller disconnected components.
This repository supports the transition-network component of the broader study:
A Minimal Mechanism in Structured Agent-Based Landscapes* (2026)
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Newman, M. E. J. (2018). Networks: An Introduction. Oxford University Press.
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Barabási, A.-L. (2016). Network Science. Cambridge University Press.
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Stauffer, D., & Aharony, A. (2003). Introduction to Percolation Theory. Taylor & Francis.
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Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D.-U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4–5), 175–308.
Fabio Nelli
Independent researcher in complex systems and agent-based modeling.
Project developed under the Meccanismo Complesso initiative.