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logit-graph 2025

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logit-graph demo
Synthetic temporal logit graph: nodes arrive over time and attach preferentially to high-degree nodes, so hubs emerge as the network grows.

A Python package to fit, simulate, and compare logit graph models against the classic random-graph baselines — Erdős–Rényi (ER), Watts–Strogatz (WS), and Barabási–Albert (BA) — using a spectral Graph Information Criterion (GIC). Published on PyPI as logit-graph with a scikit-learn-style API and reproducible, seedable comparisons.

pip install "logit-graph>=0.1.3"

What it does

  • Estimate — pick the neighborhood depth d̂ via AIC and the intercept σ̂ (offset logit) from a real graph.
  • Generate — sample graphs whose normalized-Laplacian spectrum matches the data, via a GIC-guided Gibbs sampler.
  • Compare — rank the logit graph against ER / WS / BA on the same spectral GIC (lower is better).

Results at a glance

Reproducible comparison on the SNAP Facebook ego network 686 (random_state=0):

Model GIC ↓ Notes
Logit Graph ~4.07 AIC-selected d̂, offset-logit σ̂
BA ~4.12 preferential-attachment grid search
WS ~4.57 small-world grid search
ER ~5.78 density-matched

The logit graph wins on this network — its degree-aware edge model captures spectral structure the classic baselines miss.

A 60-second taste 

from logit_graph import simulate_graph, select_d_ensemble, estimate_sigma_from_graph

adj, meta = simulate_graph(
    200, 1, sigma=-4.0, n_iter=30_000,
    feature_mode="incremental", target_density=0.10, seed=42, return_meta=True,
)
d_hat, _ = select_d_ensemble([adj], [0, 1, 2, 3], "incremental")
sigma_hat = estimate_sigma_from_graph(adj, d_hat, "incremental")
print(f"d_hat={d_hat}, sigma_hat={sigma_hat:.3f}")

Core API

  • simulate_graph — generate a logit graph at (n, d, σ)
  • select_d_ensemble — AIC model selection over the depth d
  • estimate_sigma_from_graph — offset-logit σ̂ at fixed d
  • GraphModelComparator — logit graph vs baselines, scored by spectral GIC
  • LogitGraphFitter — fixed-d spectral fitter

The repo also ships an extensive experiment suite (reproducible make targets for parameter recovery, ROC power analysis, MCMC convergence diagnostics, and real-network GIC comparisons on Facebook, Twitch, arXiv, and animal connectomes), plus a newer temporal logit graph for growing networks.