The dynamics of network social contagion processes such as opinion formation and epidemic spreading are often mediated by interactions between multiple nodes.
Previous results have shown that these higher-order interactions can profoundly modify the dynamics of contagion processes, resulting in bistability, hysteresis, and explosive transitions.
In this paper, we present and analyze a hyperdegree-based mean-field description of the dynamics of the SIS model on hypergraphs, i.e. networks with higher-order interactions, and illustrate its applicability with the example of a hypergraph where contagion is mediated by both Links (pairwise interactions) and Triangles (three-way interactions).
We consider various models for the organization of link and triangle structure, and different mechanisms of higher-order contagion and healing. We find that explosive transitions can be suppressed by heterogeneity in the link degree distribution, when links and triangles are chosen independently, or when link and triangle connections are positively correlated when compared to the uncorrelated case. We verify these results with microscopic simulations of the contagion process and with analytic predictions derived from the mean-field model. Our results show that the structure of higher-order interactions can have important effects on contagion processes on hypergraphs. arXiv:2006.15453 [physics]
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LANDRY, Nicholas and RESTREPO, Juan G., 2020. The effect of heterogeneity on hypergraph contagion models. Chaos: An Interdisciplinary Journal of Nonlinear Science. Online. October 2020. Vol. 30, no. 10, p. 103117. [Accessed 1 February 2023]. DOI 10.1063/5.0020034. post 
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This paper studies the dynamics of network social contagion processes in hypergraphs, networks with higher-order interactions. The authors present and analyze a hyperdegree-based mean-field description of the SIS model and illustrate its applicability with an example hypergraph. They consider various models for the organization of Link and Triangle structure and mechanisms of higher-order contagion and healing. The results show that explosive transitions can be suppressed by heterogeneity in the link degree distribution or positively correlated link and triangle connections. The results are verified with microscopic simulations and analytic predictions. The paper concludes that the structure of higher-order interactions can have important effects on contagion processes on hypergraphs.