# Local Clustering in Hypergraphs through Higher-Order Motifs

arXiv: https://arxiv.org/abs/2507.10570 · HTML: https://mlsanity.com/paper/2507.10570/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2025.

## Built on by (most cited first, 1 of 1)

- [Thresholded Local Hyper-Flow Diffusion](https://mlsanity.com/paper/2606.09340/) (2026)

## Abstract (arXiv)

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.