A new method for quantifying network cyclic structure to improve community detection

TL;DR

This paper introduces RNBRW, a novel method that quantifies cyclic structures in networks to enhance community detection, especially in sparse graphs, by assigning importance weights to edges based on cycle formation probabilities.

Contribution

The paper proposes RNBRW, a new random walk-based measure for edge importance that improves community detection performance in networks.

Findings

RNBRW effectively identifies cyclic-rich edges.

Pre-weighting with RNBRW enhances community detection accuracy.

RNBRW is computationally efficient for large, sparse graphs.

Abstract

A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local "richness" of the cyclic structure. In this paper, we introduce renewal non-backtracking random walks (RNBRW) as a way of quantifying this structure. RNBRW gives a weight to each edge equal to the probability that a non-backtracking random walk completes a cycle with that edge. Hence, edges with larger weights may be thought of as more important to the formation of cycles. Of note, since separate random walks can be performed in parallel, RNBRW weights can be estimated very quickly, even for large graphs. We give simulation results showing that pre-weighting edges through RNBRW may substantially improve the performance of common community detection algorithms. Our results suggest that RNBRW is especially efficient for the challenging case of detecting communities in sparse graphs.