Papers › Why the Metric Backbone Preserves Community Structure

Why the Metric Backbone Preserves Community Structure

6 Jun 2024arXiv:2406.03852archive 2025-07-28

Maximilien Dreveton, Charbel Chucri, Matthias Grossglauser, Patrick Thiran

The metric backbone of a weighted graph is the union of all-pairs shortest paths. It is obtained by removing all edges (u,v) that are not the shortest path between u and v. In networks with well-separated communities, the metric backbone tends to preserve many inter-community edges, because these edges serve as bridges connecting two communities, but tends to delete many intra-community edges because the communities are dense. This suggests that the metric backbone would dilute or destroy the community structure of the network. However, this is not borne out by prior empirical work, which instead showed that the metric backbone of real networks preserves the community structure of the original network well. In this work, we analyze the metric backbone of a broad class of weighted random graphs with communities, and we formally prove the robustness of the community structure with respect to the deletion of all the edges that are not in the metric backbone. An empirical comparison of several graph sparsification techniques confirms our theoretical finding and shows that the metric backbone is an efficient sparsifier in the presence of communities.

PaperPDFCode

Code

charbel-11/why-the-metric-backbone-preserves-community-structure officialmentioned in papermentioned on GitHub report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections