On the Relation between Graph Ricci Curvature and Community Structure

TL;DR

This paper explores how the curvature of edges in a network relates to its community structure, providing bounds on intercommunity edge curvature to enhance understanding of network topology.

Contribution

It establishes a theoretical link between graph Ricci curvature and community structure, offering bounds on intercommunity edge curvature.

Findings

Derived apriori bounds on intercommunity edge curvature.

Linked curvature properties to community detection.

Enhanced understanding of network topology through curvature analysis.

Abstract

The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as well. In particular, this has led to curvature-based community detection algorithms. In this paper, we reveal the relation between community structure of a network and the curvature of its edges. In particular, we give apriori bounds on the curvature of intercommunity edges of a graph.