Network clique cover approximation to analyze complex contagions through group interactions

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.

arXiv comment26 pages, 10 figures

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• Expectation-Maximizing Network Reconstruction and MostApplicable Network Types Based on Binary Time Series Data
• Effective epidemic containment strategy in hypergraphs
• Synchronization of phase oscillators on complex hypergraphs
• A triadic approximation reveals the role of interaction overlap on the spread of complex contagions on higher-order networks
• Contagion dynamics on hypergraphs with nested hyperedges
• Hypergraph assortativity: a dynamical systems perspective
• Nonlinear bias toward complex contagion in uncertain transmission settings
• Opinion disparity in hypergraphs with community structure
• Degree correlations in graphs with clique clustering
• Characteristic scales and adaptation in higher-order contagions
• Spreading dynamics in networks under context-dependent behavior
• Belief propagation on networks with cliques and chordless cycles
• Local topological moves determine global diffusion properties of hyperbolic higher-order networks