Contagion dynamics on hypergraphs with nested hyperedges

Abstract

In complex social systems encoded as hypergraphs, higher-order (i.e., group) interactions taking place among more than two individuals are represented by hyperedges. One of the higher-order correlation structures native to hypergraphs is the nestedness: Some hyperedges can be entirely contained (that is, nested) within another larger hyperedge, which itself can also be nested further in a hierarchical manner. Yet the effect of such hierarchical structure of hyperedges on the dynamics has remained unexplored. In this context, here we propose a random nested-hypergraph model with a tunable level of nestedness and investigate the effects of nestedness on a higher-order susceptible-infected-susceptible process. By developing an analytic framework called the facet approximation, we obtain the steady-state fraction of infected nodes on the random nested-hypergraph model more accurately than existing methods. Our results show that the hyperedge-nestedness affects the phase diagram significantly. Monte Carlo simulations support the analytical results.

arXiv comment8 pages, 6 figures

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Cited by in corpus (5)

• Hyperedge overlap drives explosive collective behaviors in systems with higher-order interactions
• Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs
• The simpliciality of higher-order networks
• Collective dynamics on higher-order networks
• Characteristic scales and adaptation in higher-order contagions