networkx_backbone

Backbone extraction algorithms for complex networks, built on NetworkX.

This library provides 65 functions across 9 modules for extracting backbone structures from weighted and unweighted networks.

Full documentation: https://www.brianckeegan.com/networkx_backbone/

Installation

pip install networkx-backbone

For full functionality (required for statistical tests, bipartite methods, and some structural methods):

pip install networkx-backbone[full]

Or install from source:

git clone https://github.com/brianckeegan/networkx_backbone.git
cd networkx_backbone
pip install -e ".[full]"

Modules

Module	Description	Key Functions
statistical	Hypothesis-testing methods	disparity_filter, noise_corrected_filter, marginal_likelihood_filter, ecm_filter, lans_filter, multiple_linkage_analysis
structural	Topology-based methods	global_threshold_filter, strongest_n_ties, global_sparsification, primary_linkage_analysis, edge_betweenness_filter, node_degree_filter, high_salience_skeleton, metric_backbone, ultrametric_backbone, doubly_stochastic_filter, h_backbone, modularity_backbone, planar_maximally_filtered_graph, maximum_spanning_tree_backbone
proximity	Neighborhood-similarity scoring	jaccard_backbone, dice_backbone, cosine_backbone, hub_promoted_index, hub_depressed_index, adamic_adar_index, resource_allocation_index, local_path_index, and more
hybrid	Combined approaches	glab_filter
bipartite	Bipartite projection backbones	simple_projection, hyper_projection, probs_projection, ycn_projection, sdsm, fdsm, fixedfill, fixedrow, fixedcol, backbone
unweighted	Sparsification for unweighted graphs	sparsify, lspar, local_degree
filters	Post-hoc filtering utilities	multigraph_to_weighted, threshold_filter, fraction_filter, boolean_filter, consensus_backbone
measures	Evaluation and comparison	node_fraction, edge_fraction, weight_fraction, reachability, ks_degree, ks_weight, compare_backbones
visualization	Graph comparison plotting	graph_difference, compare_graphs, save_graph_comparison

NetBone Core Coverage

Core method families used in netbone (Yassin et al., 2023) are represented here, including:

• Statistical: disparity_filter, marginal_likelihood_filter, ecm_filter, noise_corrected_filter, lans_filter, multiple_linkage_analysis
• Structural: global_threshold_filter, global_sparsification, primary_linkage_analysis, edge_betweenness_filter, high_salience_skeleton, doubly_stochastic_filter, maximum_spanning_tree_backbone
• Hybrid: glab_filter

Quick Start

import networkx as nx
import networkx_backbone as nb

# Create a weighted graph
G = nx.les_miserables_graph()

# 1) Score edges
scored = nb.disparity_filter(G)

# 2) Filter edges
backbone = nb.threshold_filter(scored, "disparity_pvalue", 0.05)

# Compare backbone to original
print(f"Edges kept: {nb.edge_fraction(G, backbone):.1%}")
print(f"Nodes kept: {nb.node_fraction(G, backbone):.1%}")

Disparity filter visualization

Proximity-based scoring

# Score edges by Jaccard similarity of endpoint neighborhoods
scored = nb.jaccard_backbone(G)

# Keep only the top 20% most structurally embedded edges
backbone = nb.fraction_filter(scored, "jaccard", 0.2, ascending=False)

Bipartite backbone

B = nx.davis_southern_women_graph()
women_nodes = [n for n, d in B.nodes(data=True) if d["bipartite"] == 0]
scored = nb.sdsm(B, agent_nodes=women_nodes, projection="hyper")
backbone = nb.threshold_filter(scored, "sdsm_pvalue", 0.05, mode="below")

Projection weights follow the simple/hyper/ProbS/YCN formulations described in Coscia & Neffke (2017).

Comparing multiple methods

backbones = {
    "disparity": nb.threshold_filter(nb.disparity_filter(G), "disparity_pvalue", 0.05),
    "mst": nb.boolean_filter(nb.maximum_spanning_tree_backbone(G), "mst_keep"),
}
results = nb.compare_backbones(G, backbones)

Dependencies

• Required: networkx >= 3.0
• Optional: numpy >= 1.23, scipy >= 1.9, matplotlib >= 3.7 (needed for statistical methods, bipartite methods, some structural/proximity methods, visualization helpers, and docs gallery generation)

Testing

pip install -e ".[test]"
pytest

Visualization gallery

Backbone visualizations in the docs are generated with Sphinx Gallery from example scripts under docs/examples/.

Build docs (including the graph comparison gallery and function-linked visualizations):

pip install -e ".[docs]"
sphinx-build -b html docs docs/_build/html

References

Key papers behind the implemented methods:

• Coscia, M. & Neffke, F. M. (2017). Network backboning with noisy data. Proc. IEEE ICDE, 425-436.
• Coscia, M. & Neffke, F. M. (2017). Network backboning with noisy data (arXiv:1906.09081).
• Girvan, M., & Newman, M. E. J. (2002). Community structure in social and biological networks. PNAS, 99(12), 7821-7826.
• Grady, D., Thiemann, C., & Brockmann, D. (2012). Robust classification of salient links in complex networks. Nature Communications, 3, 864.
• Hamann, M., Lindner, G., Meyerhenke, H., Staudt, C. L., and Wagner, D. (2016). Structure-Preserving Sparsification Methods for Social Networks. Social Network Analysis and Mining, 6, 22.
• Simas, T., Correia, R. B., & Rocha, L. M. (2021). The distance backbone of complex networks. J. Complex Networks, 9(6), cnab021.
• Neal, Z. P. (2014). The backbone of bipartite projections. Social Networks, 39, 84-97.
• Neal, Z. P. (2022). backbone: An R package to extract network backbones. PLoS One, 17(5), e0269137.
• Satuluri, V., Parthasarathy, S., & Ruan, Y. (2011). Local graph sparsification for scalable clustering. SIGMOD, 721-732.Serrano, M. A., Boguna, M., & Vespignani, A. (2009). Extracting the multiscale backbone of complex weighted networks. PNAS, 106(16), 6483-6488.
• Van Nuffel, N., Heyndrickx, C., & Wets, G. (2010). Measuring hierarchy and reciprocity in networks.
• Yassin, A., Haidar, A., Cherifi, H., Seba, H., & Togni, O. (2023). An evaluation tool for backbone extraction techniques in weighted complex networks. Scientific Reports, 13, 17000.
• Yassin A., Cherifi, H., Seba, H., & Togni, O. (2025). Backbone extraction through statistical edge filtering: A comparative study. PLoS One, 20(1): e0316141.
• Yassin A., Cherifi, H., Seba, H., & Togni, O. (2025). Exploring weighted network backbone extraction: A comparative analysis of structural techniques. PLoS One, 20(5): e0322298.

Other libraries and datasets:

• Yassin, A., Haidar, A., Cherifi, H., Seba, H., & Togni, O. (2023). netbone.
• Yassin, A., et al. (2025). structural-backbone-methods-comparison.
• Neal, Z. (2022). backbone.
• Chrol, B. & Bojanowski, M. (2018). Proximity-based Methods for Link Prediction.

License

BSD 3-Clause License. See LICENSE for details.