Hypergraph clustering using Ricci curvature: an edge transport perspective

Olympio Hacquard

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arXiv · 2412.15695

Hypergraph clustering using Ricci curvature: an edge transport perspective

Olympio Hacquard

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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.

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Olympio Hacquard. 2024-12-20. Hypergraph clustering using Ricci curvature: an edge transport perspective. https://arxiv.org/abs/2412.15695

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