Hypergraph Mining via Proximity Matrix

2026-04-21

AI Summary

Traditional hypergraph incidence matrices employ binary representations, which struggle to capture the complex higher-order relationships between nodes and hyperedges arising from their size disparities. This work proposes the first continuous node–hyperedge proximity matrix grounded in a resource allocation mechanism, overcoming the limitations of binary encoding and enabling a more refined modeling of higher-order interactions. The resulting proximity matrix can be seamlessly integrated into lightweight algorithms to effectively support downstream tasks such as link prediction, key node identification, and community detection. Extensive experiments on multiple real-world hypergraph datasets demonstrate that methods leveraging this matrix consistently outperform existing baselines across all three core tasks, confirming both its expressive power and practical utility.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Hypergraphs serve as an effective tool widely adopted to characterize higher-order interactions in complex systems. The most intuitive and commonly used mathematical instrument for representing a hypergraph is the incidence matrix, in which each entry is binary, indicating whether the corresponding node belongs to the corresponding hyperedge. Although the incidence matrix has become a foundational tool for hypergraph analysis and mining, we argue that its binary nature is insufficient to accurately capture the complexity of node-hyperedge relationships arising from the fact that different hyperedges can contain vastly different numbers of nodes. Accordingly, based on the resource allocation process on hypergraphs, we propose a continuous-valued matrix to quantify the proximity between nodes and hyperedges. To verify the effectiveness of the proposed proximity matrix, we investigate three important tasks in hypergraph mining: link prediction, vital nodes identification, and community detection. Experimental results on numerous real-world hypergraphs show that simply designed algorithms centered on the proximity matrix significantly outperform benchmark algorithms across these three tasks.

Problem

• hypergraph
• incidence matrix
• higher-order interactions
• node-hyperedge relationship
• proximity

Innovation

• hypergraph mining
• proximity matrix
• resource allocation
• higher-order interactions
• incidence matrix