Network clique cover approximation to analyze complex contagions through group interactions

TL;DR

This paper introduces a discrete-time model for complex contagions in networks with group interactions, using clique covers to account for higher-order correlations, revealing new insights into contagion dynamics.

Contribution

It presents a novel approach employing clique covers and heuristics to model higher-order interactions in complex contagions, extending understanding beyond mean-field models.

Findings

Higher-order correlations influence the critical point of contagion.

Structured populations can exhibit bi-stability in contagion dynamics.

Mean-field models cannot capture the dependence on higher-order couplings.

Abstract

Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections of all-to-all pair-wise interactions (cliques) and/or group interactions, involving many of their members at once. In this work, focusing on interaction structures represented as simplicial complexes, we present a discrete-time microscopic model of complex contagion for a susceptible-infected-susceptible dynamics. Introducing a particular edge clique cover and a heuristic to find it, the model accounts for the higher-order dynamical correlations among the members of the substructures (cliques/simplices). The analytical computation of the critical point reveals that higher-order correlations are responsible for its dependence on the higher-order couplings. While such dependence eludes any mean-field model, the possibility of a bi-stable region is extended to structured populations.