Disentangling high-order mechanisms and high-order behaviours in complex systems

TL;DR

This paper discusses the importance of integrating hypergraph models and information-theoretic tools to better understand high-order interactions in complex systems, emphasizing a comprehensive approach that combines both methods.

Contribution

It clarifies that hypergraph topological analysis and information-theoretic methods are complementary, advocating for their combined use to study high-order phenomena in complex systems.

Findings

Hypergraph models capture multi-element interactions.

Information-theoretic tools quantify high-order dependencies.

Combining both approaches provides a more complete understanding.

Abstract

Battiston et al. (arXiv:2110.06023) provide a comprehensive overview of how investigations of complex systems should take into account interactions between more than two elements, which can be modelled by hypergraphs and studied via topological data analysis. Following a separate line of enquiry, a broad literature has developed information-theoretic tools to characterize high-order interdependencies from observed data. While these could seem to be competing approaches aiming to address the same question, in this correspondence we clarify that this is not the case, and that a complete account of higher-order phenomena needs to embrace both.