MENoBiS

MENoBiS fits maximum-entropy null models for directed non-binary networks: it models integer node-pair occupations \(t_{ij}\), fits structural constraints in expectation or exactly, samples null ensembles, and flags statistically surprising node pairs.

What MENoBiS does

1. Fit null models — ME, B, and W occupation families under grand-canonical, canonical, and microcanonical ensembles, with six structural constraint types (strengths, degrees, occupied-pair counts, total events, pair costs, and their combinations).
2. Sample null ensembles — exact direct samplers and validated stationary-MCMC kernels; use the draws to compare observed network statistics with the null.
3. Filter observed node pairs — per-pair p-values against the fitted null, with multiple-testing corrections and absent-edge detection.

Minimal vocabulary

• non-binary network — a directed network with integer pair occupations \(t_{ij}\);
• occupation number \(t_{ij}\) — integer event count on pair \((i,j)\);
• occupied pair — a pair with \(t_{ij}>0\);
• binary support — the indicator \(a_{ij}=\mathbf 1[t_{ij}>0]\);
• strength / degree — occupation / support sums per node.

See Notation for the full symbol table.

Start here by task

Goal	Start here
Install and run the first fit/sample pipeline	Getting started
Decide which null model to use	Choose a model
What is actually supported today	Supported models
Fit and sample a model	Fit and sample
Walk through a compact applied overview	Main use cases
Filter significant node pairs	Filter node pairs
Understand the mathematics	Scientific foundations
Runtime and memory expectations	Practical scaling
Work on the code	Development

Installation status

Source/development installation (Rust toolchain required; not yet on PyPI):

git clone https://github.com/uladribia/menobis.git
cd menobis
uv sync
uv run maturin develop --release -m crates/menobis-python/Cargo.toml
uv run menobis --version

This is a source/development installation, not a generic package install.

One tiny example

from menobis.analysis import compute_all_stats
from menobis.models import Constraint, Ensemble, ModelFamily, fit_model
from menobis.routing import sample_model
from menobis.utilities.synthetic import (
    derive_synthetic_constraints,
    generate_pa_geographic_network,
)

network = generate_pa_geographic_network(30, average_degree=6.0, seed=7)
c = derive_synthetic_constraints(network)

fit = fit_model(
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH,
    strength_out=c.strength_out,
    strength_in=c.strength_in,
)
assert fit.converged

sample = sample_model(
    ensemble=Ensemble.GRAND_CANONICAL,
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH,
    fit=fit,
    seed=0,
)
print(compute_all_stats(sample).y2_out.mean())

This example is executable — the full pipeline is in Getting started.

About

MENoBiS implements the non-binary maximum-entropy framework of Oleguer Sagarra's doctoral thesis (see References and thesis).

The codebase is Rust for computation with thin typed Python wrappers; see Architecture for contributors.

Agentic coding disclosure

MENoBiS was coded and documented with help from agentic coding workflows using the Pi coding agent and several LLM providers. Human maintainers directed, reviewed, tested, and accepted the changes.