Network clique cover approximation to analyze complex contagions through group interactions

Identifier:  imarina:9217197

Handle: https://hdl.handle.net/20.500.11797/imarina9217197

Authors:  Burgio, Giulio; Arenas, Alex; Gomez, Sergio; Matamalas, Joan T

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. Higher-order contagion models capture opinion dynamics and adoption of behavior in social networks. In this paper, the authors propose a mathematical framework able to accurately characterize the phase diagram of these contagion processes in social higher-order networks.