Mixed-Membership Community Detection via Line Graph Curvature

Yu Tian, Zachary Lubberts, Melanie Weber

Keywords: Line Graph, Mixed-membership community detection, Ollivier-Ricci curvature, Curvature-based Network Analysis

TL;DR: We propose an algorithm for mixed-membership community detection on the line graph via discrete Ricci curvature.

Abstract:

Community detection is a classical method for understanding the structure of relational
data. In this paper, we study the problem of identifying mixed-membership community
structure. We argue that it is beneficial to perform this task on the line graph, which can
be constructed from an input graph by encoding the relationship between its edges. Here,
we propose a curvature-based algorithm for mixed-membership community detection on
the line graph. Our algorithm implements a discrete Ricci curvature flow under which the
edge weights of a graph evolve to reveal its community structure. We demonstrate the
performance of our approach in a series of benchmark experiments.