Community and hyperedge inference in multiple hypergraphs

2025-05-08

AI Summary

This work addresses the problem of modeling multi-hypergraph systems, where multiple high-order networks coexist and exhibit structural heterogeneity. We propose the first unified joint modeling framework that integrates structural information across distinct hypergraphs to enhance community detection, arbitrary-scale missing hyperedge prediction, and cross-hypergraph edge inference. Methodologically, we introduce the novel concept of *intra-hyperedge degree* to quantify heterogeneous node contributions to hyperedge formation; design a scalable stochastic block model (SBM) that uniformly supports both single- and multi-type hypergraphs—including settings without inter-hypergraph connections; and employ variational inference coupled with likelihood optimization for efficient learning. Evaluated on multiple real-world higher-order datasets, our approach consistently outperforms state-of-the-art baselines across all three tasks—community detection, hyperedge completion, and cross-hypergraph link prediction—achieving new SOTA results. This demonstrates its strong adaptability and generalization capability for heterogeneous multi-hypergraph systems.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding relationship between genes and their protein products, drive the establishment of interconnections between multiple hypergraphs. Here, we demonstrate how to utilize those interconnections between multiple hypergraphs to synthesize integrated information from multiple higher-order systems, thereby enhancing understanding of underlying structures. We propose a model based on the stochastic block model, which integrates information from multiple hypergraphs to reveal latent high-order structures. Real-world hyperedges exhibit preferential attachment, where certain nodes dominate hyperedge formation. To characterize this phenomenon, our model introduces hyperedge internal degree to quantify nodes' contributions to hyperedge formation. This model is capable of mining communities, predicting missing hyperedges of arbitrary sizes within hypergraphs, and inferring inter-hypergraph edges between hypergraphs. We apply our model to high-order datasets to evaluate its performance. Experimental results demonstrate strong performance of our model in community detection, hyperedge prediction, and inter-hypergraph edge prediction tasks. Moreover, we show that our model enables analysis of multiple hypergraphs of different types and supports the analysis of a single hypergraph in the absence of inter-hypergraph edges. Our work provides a practical and flexible tool for analyzing multiple hypergraphs, greatly advancing the understanding of the organization in real-world high-order systems.

Problem

• Inferring communities and hyperedges in interconnected hypergraphs
• Modeling preferential attachment in hyperedge formation
• Integrating multiple hypergraphs to reveal latent structures

Innovation

• Stochastic block model integrates multiple hypergraphs information
• Hyperedges internal degree quantifies nodes' contributions
• Model mines communities and predicts missing hyperedges