# Opinion disparity in hypergraphs with community structure

## TL;DR

This paper investigates how higher-order interactions in hypergraphs with community structure can lead to persistent opinion disparities between communities, highlighting the influence of community structure and interaction types.

## Contribution

It introduces a hypergraph model with community structure and analyzes opinion spread, revealing the impact of higher-order interactions on opinion disparity.

## Key findings

- Opinion disparity depends on community structure strength.
- Disparities are more sensitive to triangle interactions than links.
- Community size differences significantly affect opinion disparities.

## Abstract

The division of a social group into subgroups with opposing opinions, which we refer to as opinion disparity, is a prevalent phenomenon in society. This phenomenon 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 opinion disparity 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 this opinion disparity can exist and find that the existence of these disparities is much more sensitive to the triangle community structure than to the link community structure. We show that the existence and type of opinion disparities are extremely sensitive to differences in the sizes of the two communities.