Filter a network

TL;DR

Fit an independent grand-canonical null model, then classify observed node pairs as upper-significant, lower-significant, or compatible.

Choose a starting null

Data assumption	Recommended first model
Distinguishable trips/events, no cost data	ME strength
Distinguishable trips/events with projected coordinates	ME strength-cost
Binary support is part of the hypothesis	ME strength-degree or strength-edges
Bounded layers per pair	B family with layers=M
Indistinguishable events	W family; check convergence notes first

Why ME for origin-destination trips?

If trips are individual distinguishable events, the ME/Poisson family is the natural first null. Switch families only when event nature changes.

Python example

from menobis.filtering import filter_model
from menobis.models import Constraint, ModelFamily, fit_model
from menobis.utilities.synthetic import (
    derive_synthetic_constraints,
    generate_pa_geographic_network,
)

network = generate_pa_geographic_network(30, average_degree=6.0, seed=11)
constraints = derive_synthetic_constraints(network)

fit = fit_model(
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH_COST,
    strength_out=constraints.strength_out,
    strength_in=constraints.strength_in,
    target_cost=constraints.total_cost,
    coord_x=network.x,
    coord_y=network.y,
    self_loops=False,
)

result = filter_model(
    network.edges,
    family=ModelFamily.ME,
    constraint=Constraint.STRENGTH_COST,
    fit=fit,
    coord_x=network.x,
    coord_y=network.y,
    alpha=0.05,
    tail="upper",
)

print(result.upper.edges.num_edges)

Interpret the result

Field	Meaning
upper	observed pairs with occupations larger than expected
lower	positive observed pairs with occupations smaller than expected
compatible	observed pairs not rejected by the test
absent_lower	absent pairs that should likely exist; opt-in with detect_absent=True

FilteredEdges also stores upper_pvalue, lower_pvalue, expected occupation, and occupation probability for each reported pair.

CLI example

uv run menobis filter strength-poisson edges.csv \
  --alpha 0.05 --tail upper --output-prefix filtered/

For spatial costs, provide projected coordinates:

uv run menobis filter strength-cost-poisson edges.csv \
  --coordinates xy.csv --target-cost 120.0 --output-prefix filtered/

Next step

Use Sample ensemble magnitudes to test whether a network-level statistic is special, not just individual pairs.