Local Clustering in Hypergraphs through Higher-Order Motifs

TL;DR

This paper introduces a novel hypergraph clustering method based on higher-order motifs, improving local clustering quality by capturing complex interactions and comparing two strategies for cluster identification.

Contribution

It extends motif-based clustering techniques to hypergraphs, proposing core-based and BFS-based strategies for local clustering around seed hyperedges.

Findings

The framework effectively captures higher-order interactions in hypergraphs.

Both clustering strategies outperform traditional methods in quality and efficiency.

Experiments demonstrate the method's applicability to real-world datasets.

Abstract

Hypergraphs provide a powerful framework for modeling complex systems and networks with higher-order interactions beyond simple pairwise relationships. However, graph-based clustering approaches, which focus primarily on pairwise relations, fail to represent higher-order interactions, often resulting in low-quality clustering outcomes. In this work, we introduce a novel approach for local clustering in hypergraphs based on higher-order motifs, small connected subgraphs in which nodes may be linked by interactions of any order, extending motif-based techniques previously applied to standard graphs. Our method exploits hypergraph-specific higher-order motifs to better characterize local structures and optimize motif conductance. We propose two alternative strategies for identifying local clusters around a seed hyperedge: a core-based method utilizing hypergraph core decomposition and a BFS-based method based on breadth-first exploration. We construct an auxiliary hypergraph to facilitate efficient partitioning and introduce a framework for local motif-based clustering. Extensive experiments on real-world datasets demonstrate the effectiveness of our framework and provide a comparative analysis of the two proposed clustering strategies in terms of clustering quality and computational efficiency.