Hypergraph backboning

2026-05-30

AI Summary

This work addresses the challenge of concisely characterizing high-order interactions in complex systems represented by high-dimensional hypergraphs, which are often hindered by structural redundancy. To this end, the authors propose a nonparametric, information-theoretic framework for hypergraph skeleton extraction that prunes nested or redundant hyperedges to yield a minimal weighted hypergraph representation. This representation preserves both local heterogeneity and essential high-order structures. The method uniquely integrates information theory with nonparametric statistics, jointly accounting for topological organization and edge weights. Evaluated on both synthetic and real-world datasets spanning multiple domains, the approach achieves substantial sparsification while faithfully retaining the core high-order interactions without loss of critical structural information.

Abstract

Hypergraphs provide a natural framework for describing complex networked systems with higher-order, non-dyadic interactions. Due to their high dimensionality and often redundant structure, a key challenge is to develop methods that simplify hypergraph representations while preserving the essential structure of interactions. Here we present a principled, efficient, and non-parametric information-theoretic method for pruning nested and/or redundant structures in hypergraphs, enabling a minimal representation of higher-order interactions in the presence of local heterogeneity. Our approach naturally extends to weighted hypergraphs, where higher-order topology and hyperedge weights combine to identify the system's structural backbone. We validate the method on controlled synthetic hypergraphs and apply it to empirical datasets from diverse domains, demonstrating substantial sparsification without loss of core structural information.

Problem

• hypergraph
• backboning
• redundancy
• higher-order interactions
• sparsification

Innovation

• hypergraph backboning
• information-theoretic pruning
• higher-order interactions
• structural sparsification
• weighted hypergraphs