Local Clustering in Hypergraphs through Higher-Order Motifs

2025-07-09

AI Summary

Existing hypergraph clustering methods predominantly model pairwise relationships, failing to capture higher-order interactions and thus limiting local clustering quality. This paper introduces higher-order motifs into hypergraph local clustering for the first time, proposing a novel framework grounded in motif conductance. Specifically, it constructs a motif-augmented hypergraph and identifies local clusters via two complementary strategies: core decomposition and breadth-first search. By explicitly modeling higher-order cooperative structures among hyperedges, the approach enhances expressiveness for complex dependencies. Extensive experiments on multiple real-world datasets demonstrate that the method significantly improves clustering quality while achieving a favorable trade-off between accuracy and efficiency. Moreover, it offers an interpretable and scalable paradigm for hypergraph local clustering—advancing beyond conventional pairwise abstractions toward principled higher-order structural modeling.

Technology Category

• Machine Learning: Clustering
• Search and Optimization: Local Search
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Hypergraph clustering lacks higher-order interaction representation
• Existing graph methods yield low-quality clustering outcomes
• Novel motif-based approach improves local clustering accuracy

Innovation

• Uses higher-order motifs for hypergraph clustering
• Introduces core-based and BFS-based clustering strategies
• Constructs auxiliary hypergraph for efficient partitioning