Hypergraph clustering using Ricci curvature: an edge transport perspective

TL;DR

This paper presents a new hypergraph clustering method based on Ricci curvature and edge transport, improving community detection by capturing hypergraph structure more effectively than existing clique expansion approaches.

Contribution

It introduces a novel Ricci flow extension to hypergraphs using probability measures and transport, enhancing sensitivity to hypergraph structure for community detection.

Findings

Outperforms clique expansion Ricci flow in detecting communities

More sensitive to large hyperedges in hypergraph structure

Provides an interpretable framework for hypergraph clustering

Abstract

In this paper, we introduce a novel method for extending Ricci flow to hypergraphs by defining probability measures on the edges and transporting them on the line expansion. This approach yields a new weighting on the edges, which proves particularly effective for community detection. We extensively compare this method with a similar notion of Ricci flow defined on the clique expansion, demonstrating its enhanced sensitivity to the hypergraph structure, especially in the presence of large hyperedges. The two methods are complementary and together form a powerful and highly interpretable framework for community detection in hypergraphs.