Network clique cover approximation to analyze complex contagions through group interactions

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