Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition

TL;DR

This paper analyzes how homophily and heterophily influence the structure of preferred-degree networks, revealing an overwhelming transition where smaller community members become dominated by links from larger groups, using mean-field theory and simulations.

Contribution

It introduces a mean-field analytical framework to study the effects of homophily/heterophily on dynamic networks with fixed opinions and preferred degrees, highlighting the overwhelming transition phenomenon.

Findings

Heterophily induces an overwhelming transition in network structure.

Small communities become dominated by larger groups under high heterophily.

Network degree distributions and polarization depend on community sizes and homophily levels.

Abstract

We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents' opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped by homophily/heterophily, which is a form of social interaction by which individuals tend to establish links with others having similar/dissimilar opinions. Using Monte Carlo simulations and a detailed mean-field analysis, we study in detail how the sizes of the communities and the degree of homophily/heterophily affects the network structure. In particular, we show that when the network is subject to enough heterophily, an "overwhelming transition" occurs: individuals of the smaller community are overwhelmed by links from agents of the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by obtaining the network's total and joint degree distributions, as well as the fraction of links across both communities and that of agents having fewer edges than the preferred degree. We use our mean-field theory to discuss the network's polarization when the group sizes and level of homophily vary.