Polarization in hypergraphs with community structure

Opinion polarization, the division of a social group into subgroups with opposing opinions, is a prevalent phenomenon in society. The spontaneous formation of polarization has been modeled by including mechanisms such as opinion homophily, bounded confidence interactions, and social reinforcement mechanisms. In this paper we study a complementary mechanism for the formation of polarization in networks with community structure based on higher-order interactions, i.e., simultaneous interactions between multiple agents. We present an extension of the planted partition model for uniform hypergraphs as a simple model of community structure and consider the hypergraph SIS model on a hypergraph with two communities where the binary ideology can spread via links (pairwise interactions) and triangles (three-way interactions). We approximate this contagion process with a mean-field model and find that for strong enough community structure, the two communities can hold very different average opinions. We determine the regimes of structural and infectious parameters for which polarization can exist and find that the existence of polarization is much more sensitive to the triangle community structure than to the link community structure. We show that the existence and type of polarization is extremely sensitive to differences in size between the two communities.