Community Detection on Networks with Ricci Flow

TL;DR

This paper introduces a novel geometric method for community detection in networks using Ricci flow, leveraging curvature and geometric decomposition to identify communities more effectively than traditional approaches.

Contribution

It presents a new geometric approach applying Ricci flow to network community detection, bridging differential geometry and network analysis.

Findings

Effective identification of communities in networks with ground-truth structures

Demonstrated superiority over traditional statistical and combinatorial methods

Validated approach through experiments on real-world networks

Abstract

Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications. While existing approaches mainly apply statistical or graph theoretical/combinatorial methods for community detection, in this paper, we present a novel geometric approach which enables us to borrow powerful classical geometric methods and properties. By considering networks as geometric objects and communities in a network as a geometric decomposition, we apply curvature and discrete Ricci flow, which have been used to decompose smooth manifolds with astonishing successes in mathematics, to break down communities in networks. We tested our method on networks with ground-truth community structures, and experimentally confirmed the effectiveness of this geometric approach.