Social contagion models on simplicial complexes and hypergraphs

Giovanni Petri


Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Thanks to network descriptions, our understanding of the dynamics of such systems has increased significantly in the last two decades. However, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we first introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena, such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems. We then drop the restriction to simplicial complexes for the structure underlying the spreading, and provide both an analytical framework and numerical results for arbitrary hypergraphs. Our analyses show that this model has a vast parameter space, with first and second-order transitions, bi-stability, and hysteresis. Phenomenologically, we also extend the concept of latent heat to social contexts, which might help understanding oscillatory social behaviors. We conclude with an outlook on high-order model, posing new questions and paving the way for modeling dynamical processes on these networks.

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