Network clique cover approximation to analyze complex contagions through group interactions

Giulio Burgio,Joan T Matamalas,Sergio Gómez,Alex Arenas

doi:10.1038/s42005-021-00618-z

Giulio Burgio, Joan T Matamalas + Show 2 more

Open Access

https://doi.org/10.1038/s42005-021-00618-z

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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.

Highlights

Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them
From few years on, a growing branch of literature dedicated to the study of various dynamical processes involving group interactions12–18, has been showing that such interactions can heavily affect the dynamics, and neglecting them can lead to wrong predictions
We are interested in complex contagion processes22–26, in which the outcome of a potentially spreading interaction depends on how many different contagious agents take part to it, and not—as in simple contagions—only on the strength of the interaction

Summary

Introduction

Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Given a clique, no matter whether it conveys (g = 1) or not (g = 0) group interactions, we want to account for the dynamical correlations among the states of the nodes in it.

Results

Conclusion