Hypergraph backboning

AIPR assessment

Problem difficulty: moderately hard and emerging, with a real but not saturated prior literature on graph sparsification, hypergraph filtering, and higher-order summarization. The paper’s strengths reinforce each other well: a clean MDL formalism, a clear limitation it targets, synthetic recovery studies, and broad empirical sparsification results, plus open code in Hypergraphx. The main weaknesses also interact: the optimizer is heuristic, the empirical validation is mostly within the authors’

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.

Score Breakdown

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