Structural reducibility of hypergraphs

TL;DR

This paper introduces an information-theoretic framework to identify and reduce redundancies in hypergraph representations of complex systems, preserving essential higher-order interactions while simplifying analysis.

Contribution

It provides a novel method for assessing and simplifying hypergraph structures by pinpointing critical higher-order interactions to retain core information.

Findings

Framework effectively identifies redundant higher-order interactions.

Reductions preserve key structural information.

Method improves interpretability and computational efficiency.

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.