Homophily-based social group formation in a spin-glass self-assembly framework

TL;DR

This paper introduces a spin-glass-inspired model to explain social group formation based on homophily, revealing phase transitions and matching empirical group-size distributions in online communities.

Contribution

It presents a novel spin-glass framework for social self-assembly, analytically deriving group-size distributions and phase behavior related to homophily.

Findings

Identifies a phase transition between ordered and disordered social states.

Derives a group-size distribution matching empirical data.

Shows a first-order transition to disordered phase.

Abstract

Homophily, the tendency of humans to attract each other when sharing similar features, traits, or opinions has been identified as one of the main driving forces behind the formation of structured societies. Here we ask to what extent homophily can explain the formation of social groups, particularly their size distribution. We propose a spin-glass-inspired framework of self-assembly, where opinions are represented as multidimensional spins that dynamically self-assemble into groups; individuals within a group tend to share similar opinions (intra-group homophily), and opinions between individuals belonging to different groups tend to be different (inter-group heterophily). We compute the associated non-trivial phase diagram by solving a self-consistency equation for 'magnetization' (combined average opinion). Below a critical temperature, there exist two stable phases: one ordered with non-zero magnetization and large clusters, the other disordered with zero magnetization and no clusters. The system exhibits a first-order transition to the disordered phase. We analytically derive the group-size distribution that successfully matches empirical group-size distributions from online communities.