Dynamics on higher-order networks: A review

TL;DR

This review discusses the emergence and importance of higher-order networks in modeling complex systems, highlighting recent advances in understanding their unique dynamics across various scientific fields.

Contribution

It provides a comprehensive overview of the recent developments in higher-order network dynamics and identifies key open challenges and future research directions.

Findings

Higher-order networks capture complex group interactions beyond pairwise links.

New dynamical phenomena emerge on higher-order networks, such as novel synchronization and contagion patterns.

The review highlights the importance of higher-order models in social, biological, and technological systems.

Abstract

Network science has evolved into an indispensable platform for studying complex systems. But recent research has identified limits of classical networks, where links connect pairs of nodes, to comprehensively describe group interactions. Higher-order networks, where a link can connect more than two nodes, have therefore emerged as a new frontier in network science. Since group interactions are common in social, biological, and technological systems, higher-order networks have recently led to important new discoveries across many fields of research. We here review these works, focusing in particular on the novel aspects of the dynamics that emerges on higher-order networks. We cover a variety of dynamical processes that have thus far been studied, including different synchronization phenomena, contagion processes, the evolution of cooperation, and consensus formation. We also outline open challenges and promising directions for future research.