The effect of heterogeneity on hypergraph contagion models

TL;DR

This paper develops a mean-field model for contagion dynamics on hypergraphs with higher-order interactions, revealing how heterogeneity influences explosive transitions and contagion behavior.

Contribution

It introduces a hyperdegree-based mean-field framework for hypergraph contagion models, analyzing the impact of heterogeneity and correlation in higher-order interactions.

Findings

Heterogeneity can suppress explosive contagion transitions.

Positive correlation between links and triangles affects contagion dynamics.

Mean-field predictions align with microscopic simulations.

Abstract

The dynamics of network social contagion processes such as opinion formation and epidemic spreading are often mediated by interactions between multiple nodes. Previous results have shown that these higher-order interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions. In this paper, we present and analyze a hyperdegree-based mean-field description of the dynamics of the SIS model on hypergraphs, i.e. networks with higher-order interactions, and illustrate its applicability with the example of a hypergraph where contagion is mediated by both links (pairwise interactions) and triangles (three-way interactions). We consider various models for the organization of link and triangle structure, and different mechanisms of higher-order contagion and healing. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution, when links and triangles are chosen independently, or when link and triangle connections are positively correlated when compared to the uncorrelated case. We verify these results with microscopic simulations of the contagion process and with analytic predictions derived from the mean-field model. Our results show that the structure of higher-order interactions can have important effects on contagion processes on hypergraphs.