The physics of higher-order interactions in complex systems

TL;DR

This paper discusses the importance of higher-order interactions in complex systems, emphasizing their role in collective behaviors and outlining key challenges in understanding these systems beyond traditional pairwise network models.

Contribution

It highlights recent evidence of higher-order interactions influencing collective behaviors and identifies three major challenges for the physics of such systems.

Findings

Higher-order interactions induce collective behaviors.

Hypergraphs and simplicial complexes better model real systems.

Three key challenges outlined for future research.

Abstract

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by higher-order interactions involving groups of three or more units. Higher-order structures, such as hypergraphs and simplicial complexes, are therefore a better tool to map the real organization of many social, biological and man-made systems. Here, we highlight recent evidence of collective behaviours induced by higher-order interactions, and we outline three key challenges for the physics of higher-order systems.