A study of diffusion in network with multi-body interactions using Hypergraphs

TL;DR

This paper explores how hypergraphs can model multi-body interactions in dynamical networks, revealing that pairwise approximations may lead to incorrect conclusions, and investigates synchronization phenomena with real-world examples.

Contribution

It introduces hypergraph-based models for multi-body interactions in dynamical networks and demonstrates their importance over traditional pairwise approaches.

Findings

Hypergraph models capture multi-body interactions more accurately.

Pairwise approximations can lead to incorrect synchronization results.

Real-world examples validate the theoretical insights.

Abstract

Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids our proposed dynamical network models to go beyond the traditional archetype of only pairwise interactions. We introduce some matrices associated with hypergraphs to incorporate multi-body frameworks in dynamic networks. We illustrate the fact that the approximation of multi-body interactions by pairwise binary interactions, i.e. considering graph as the underlying architecture of the corresponding dynamical network may lead to a wrong conclusion to the study. Here we use weighted hypergraphs to deal with the multi-body interactions of variable weights. We study the possibility of global and local synchronization in discrete and continuous-time dynamical networks. Some real-world numerical illustrations are included at the end to reinforce our theoretical results.