netpol

Measure polarization in (multilayer) social networks.

Given a network -- or a dict of per-layer networks -- netpol selects the top influencers, scores every user on a bipolar latent-ideology axis via correspondence analysis, and tests whether the resulting score distribution is multimodal (polarized) using Hartigan's dip test, with optional Benjamini-Hochberg FDR correction across layers.

The method follows Falkenberg et al. (2021) and Flamino et al. (2021).

Install

pip install netpol

For local development:

git clone https://github.com/alessiogandelli/netpol && cd netpol
poetry install
poetry run pytest

Edge convention

Fixed and non-negotiable:

a -> b means "a retweets/endorses b".

Pass networkx.DiGraphs only (undirected graphs and MultiDiGraphs raise TypeError). A multilayer network is just dict[layer_id, DiGraph].

Quickstart

import networkx as nx
from netpol import PolarizationConfig, analyze, LatentIdeologyScorer

def polarized_network():           # two camps, each retweeting one influencer
    g = nx.DiGraph()
    for i in range(100):
        g.add_edge(f"c1_{i}", "inf_1")
        g.add_edge(f"c2_{i}", "inf_2")
    return g

config = PolarizationConfig(n_influencers=2, min_edges=1)
result = analyze(polarized_network(), config, LatentIdeologyScorer(min_sources=1))
print(result.is_polarized)         # True

For a multilayer network, pass a dict[layer_id, DiGraph] instead -- the same analyze call (or analyze_layers explicitly) returns a dict[layer_id, LayerResult] with FDR correction across layers:

results = analyze({"l1": layer1(), "l2": layer2()}, config)
print(results["l1"].is_polarized)

See examples/quickstart.py for a runnable version.

How it works

Per layer:

1. Select influencers -- top n_influencers nodes by in_degree (configurable) with deterministic tie-breaking.
2. Build the interaction table -- one row per edge into an influencer (['influencer', 'user']), self-loops excluded.
3. Score users -- correspondence analysis maps each user to a score in [-1, 1] on a bipolar ideology axis (the IdeologyScorer plug point; the built-in LatentIdeologyScorer is deterministic).
4. Test for polarization -- Hartigan's dip test on the score distribution.

Across layers, analyze / analyze_layers applies Benjamini-Hochberg FDR correction to the per-layer p-values and re-evaluates is_polarized against the adjusted values.

API

Everything public is importable from the package root, so netpol. autocompletes the full surface in your IDE.

Entry points:

• analyze(target, config, scorer=None) -- top-level entry point. Pass a single nx.DiGraph and get a LayerResult, or a dict[layer_id, DiGraph] and get a dict[layer_id, LayerResult] (with FDR correction).
• analyze_network(graph, config, scorer=None) -> LayerResult -- the single-network primitive.
• analyze_layers(layers, config, scorer=None) -> dict[layer_id, LayerResult] -- the multilayer orchestration.

Configuration and results:

• PolarizationConfig -- frozen config dataclass (see netpol/config.py). influencer_strategy is typed Literal["degree", "in_degree"].

• LatentIdeologyScorer(min_sources=2, max_sources=None) -- built-in scorer.

• IdeologyScorer -- Protocol to plug in your own scoring.

• LayerResult -- what you get back per network/layer:

  field	type	meaning
  layer_id	Hashable | None	layer id (None for single networks)
  n_nodes, n_edges	int	size of the analyzed graph
  influencers	list[Hashable]	selected influencer node ids
  scores	DataFrame | None	ideology scores, indexed by node id, columns score_1..score_n, values in [-1, 1]
  dip_statistic, p_value	float | None	Hartigan's dip test output
  adjusted_p_value	float | None	BH-adjusted p-value (multilayer + FDR only)
  is_polarized	bool | None	p-value (adjusted if available) below significance_level
  skip_reason	str | None	why the layer was skipped, if it was
  was_analyzed	bool	property: True iff scoring and dip test ran

Type aliases (documented in netpol/types.py) make the data shapes explicit:

• LayerId = Hashable
• Layers = dict[LayerId, nx.DiGraph]
• Results = dict[LayerId, LayerResult]
• InteractionTable = DataFrame with columns ['influencer', 'user']
• ScoreTable = DataFrame indexed by node id with columns score_1..score_n

What this does / doesn't do (yet)

Does:

• Faithful, deterministic implementation of the latent-ideology + dip-test pipeline (single-layer and multilayer).
• FDR correction, explicit skip_reason on every failure path (no silent except), directed-graph validation, min_edges guardrail.

Does not do yet (see docs/DEBATES.md for the open questions and [REVISIT] items):

• Effect-size / separation measure paired with the dip test.
• Score normalization across layers for comparison.
• Multivariate modality testing for ideology_dimensions > 1.
• Influencer-selection scope beyond per-layer (global/hybrid), adaptive pool sizing, or authority/HITS ranking.

References

• M. Falkenberg et al., "Growing polarisation around climate change on social media", arXiv:2112.12137 (2021).
• J. Flamino et al., "Shifting polarization and Twitter news influencers between two US presidential elections", arXiv:2111.02505 (2021).

License

MIT. See LICENSE.