networkx-backbone 0.1.0

Backbone extraction algorithms for complex networks

networkx_backbone

Backbone extraction algorithms for complex networks, built on NetworkX.

This library provides 47 functions across 8 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
structural	Topology-based methods	global_threshold_filter, strongest_n_ties, 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	sdsm, fdsm
unweighted	Sparsification for unweighted graphs	sparsify, lspar, local_degree
filters	Post-hoc filtering utilities	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

Quick Start

import networkx as nx
import networkx_backbone as nb

# Create a weighted graph
G = nx.karate_club_graph()
for u, v in G.edges():
    G[u][v]["weight"] = 1.0

# Extract backbone using the disparity filter
H = nb.disparity_filter(G)

# Filter to keep only significant edges (p < 0.05)
backbone = nb.threshold_filter(H, "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%}")

Proximity-based scoring

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

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

Bipartite backbone

B = nx.Graph()
B.add_edges_from([(1, "a"), (1, "b"), (2, "a"), (2, "c"), (3, "b"), (3, "c")])

backbone = nb.sdsm(B, agent_nodes=[1, 2, 3], alpha=0.05)

Comparing multiple methods

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

Dependencies

• Required: networkx >= 3.0
• Optional: numpy >= 1.23, scipy >= 1.9 (needed for statistical methods, bipartite methods, doubly stochastic filter, local path index, and KS measures)

Testing

pip install -e ".[test]"
pytest

References

Key papers behind the implemented methods:

• Coscia, M. & Neffke, F. M. (2017). Network backboning with noisy data. Proc. IEEE ICDE, 425-436.
• 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.
• Serrano, M. A., Boguna, M., & Vespignani, A. (2009). Extracting the multiscale backbone of complex weighted networks. PNAS, 106(16), 6483-6488.
• 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.