Structural Reducibility of Hypergraphs.

2025-12-12

Physical Review Letters

AI Summary

Higher-order network representations often suffer from structural redundancy, rendering them difficult to interpret and computationally expensive. This work introduces, for the first time, a systematic information-theoretic framework to quantify the structural reducibility of hypergraphs and to identify the core interactions essential for preserving the system’s higher-order structure. By selectively eliminating redundant connections while retaining critical high-order dependencies, the proposed method achieves an effective balance between parsimony and expressiveness. The approach provides a novel theoretical foundation for higher-order network analysis and demonstrates its efficacy through extensive validation on multiple real-world datasets.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Information Theory

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
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater computational demands than their pairwise counterparts. Here, we present an information-theoretic framework for determining the extent to which a hypergraph representation of a networked system is structurally redundant and for identifying its most critical higher orders of interaction that allow us to remove these redundancies while preserving essential higher-order structure.

Problem

• hypergraphs
• higher-order interactions
• structural redundancy
• information-theoretic framework

Innovation

• hypergraph
• higher-order interactions
• structural redundancy
• information-theoretic framework
• network reduction