Network clustering and community detection using modulus of families of loops

TL;DR

This paper introduces a novel network clustering measure based on the modulus of loop families, which improves community detection algorithms by quantifying loop richness and optimizing link usage.

Contribution

It presents a new loop-based clustering measure and a weighting scheme that enhances existing community detection methods.

Findings

Improves spectral partitioning performance.

Enhances modularity maximization heuristics.

Provides a new perspective on network structure through loop analysis.

Abstract

We study the structure of loops in networks using the notion of modulus of loop families. We introduce a new measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected overlap among loops by spreading the expected link-usage optimally. We propose weighting networks using these expected link-usages to improve classical community detection algorithms. We show that the proposed method enhances the performance of certain algorithms, such as spectral partitioning and modularity maximization heuristics, on standard benchmarks.