Functional Robustness

Quantify how a network’s function degrades under targeted attacks.
This library simulates dismantling trajectories driven by classical centralities (degree, betweenness, PageRank, …) and an entropy-based entanglement centrality, while tracking spectral/diffusion observables derived from the graph Laplacian.

---

Features

• Spectral entropy of a graph via Laplacian spectrum.
• Entanglement centrality: node impact measured as entropy loss after removing its incident edges.
• Functional dismantling: compare multiple strategies step-by-step and record graph/Laplacian trajectories.
• Tidy outputs for analysis + optional plotting example.

---

Install

pip install -e .

Requirements: Python ≥ 3.10, packages: networkx, numpy, scipy (examples also use matplotlib, pandas).

---

Quickstart

importnetworkxasnxfromfunctional_robustnessimportentropy, entanglement, F_Robust# Build a toy graphG=nx.erdos_renyi_graph(60, 0.08, seed=7)
beta=1.0# BaselinesH=entropy(G, beta)
ent=entanglement(G, beta)
print(f"Spectral entropy: {H:.3f}")
print("Top-3 by entanglement:", sorted(ent.items(), key=lambdax: x[1], reverse=True)[:3])
# Dismantling trajectoriescentralities, traj_graphs, traj_laps=F_Robust(G, beta=beta)

Run the end‑to‑end demo (saves a CSV + plot):

python examples/demo_functional_robustness.py

Outputs will be in ./outputs/:

• trajectory_metrics.csv
• entropy_trajectories.png

---

API (core)

entropy(G: nx.Graph, beta: float) ->float

Compute the graph’s spectral (Gibbs–Boltzmann) entropy from Laplacian eigenvalues.

entanglement(G: nx.Graph, beta: float) ->dict

Return {node: Δentropy} after removing all edges incident to node. Higher values ⇒ higher functional importance.

F_Robust(G: nx.Graph, beta: float) ->tuple[list[str], dict, dict]

Simulate dismantling using multiple centralities. Returns:

• centralities: list of strategy names
• traj_graphs: {strategy: [G_0, G_1, ...]}
• traj_laps: {strategy: [L_0, L_1, ...]}

---

Project Structure

functional_robustness/
__init__.py
entropy.py # entropy & entanglement
centrality.py # classical + functional centralities
dismantling.py # F_Robust trajectories
examples/
demo_functional_robustness.py
pyproject.toml
README.md
LICENSE

---

License

MIT © CoMuNe Lab