Community detection of hypergraphs by Ricci flow

TL;DR

This paper introduces a Ricci flow-based method for community detection in hypergraphs, leveraging higher-order interactions to improve robustness and performance in identifying functional modules.

Contribution

It develops a novel hypergraph Ricci flow framework and a community detection algorithm, HyperRCD, that directly models higher-order interactions through curvature-driven hyperedge weight evolution.

Findings

HyperRCD outperforms existing methods in robustness to topological changes.

The approach effectively captures higher-order interactions in hypergraphs.

Experimental results show competitive performance on synthetic and real-world datasets.

Abstract

Community detection in hypergraphs is both instrumental for functional module identification and intricate due to higher-order interactions among nodes. We define a hypergraph Ricci flow that directly operates on higher-order interactions of hypergraphs and prove long-time existence of the flow. Building on this theoretical foundation, we develop HyperRCD-a Ricci-flow-based community detection approach that deforms hyperedge weights through curvature-driven evolution, which provides an effective mathematical representation of higher-order interactions mediated by weighted hyperedges between nodes. Extensive experiments on both synthetic and real-world hypergraphs demonstrate that HyperRCD exhibits remarkable enhanced robustness to topological variations and competitive performance across diverse datasets.