How does homophily shape the topology of a dynamic network?

TL;DR

This paper models how homophily influences the structure of a dynamic social network with two opinions, revealing phenomena like polarization and minority oversubscription through simulations and mean-field analysis.

Contribution

It introduces a novel dynamic network model incorporating homophily with a parameter J and analyzes the resulting polarization and minority oversubscription phenomena.

Findings

Homophily parameter J influences network polarization.

Intermediate J values lead to minority oversubscription.

New polarization measure outperforms traditional edge homogeneity.

Abstract

We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by \emph{homophily}, a form of social interaction. Characterized by the parameter $J \in [-1,1]$, the latter plays a role similar to Ising spins: agents create links to others of the same opinion with probability $(1+J)/2$, and delete them with probability $(1-J)/2$. Using Monte Carlo simulations and mean-field theory, we focus on the network structure in the steady state. We study the effects of $J$ on degree distributions and the fraction of cross-party links. While the extreme cases of homophily or heterophily ($J= \pm 1$) are easily understood to result in complete polarization or anti-polarization, intermediate values of $J$ lead to interesting features of the network. Our model exhibits the intriguing feature of an "overwhelming transition" occurring when communities of different sizes are subject to sufficient heterophily: agents of the minority group are oversubscribed and their average degree greatly exceeds that of the majority group. In addition, we introduce an original measure of polarization which displays distinct advantages over the commonly used average edge homogeneity.