Homophily-Based Social Group Formation

Overview

Homophily—the tendency of humans to attract each other when sharing similar features, traits, or opinions—has been identified as a main driving force behind structured societies. This project asks to what extent homophily can explain the formation of social groups, particularly their size distribution, using a spin-glass-inspired framework where opinions dynamically self-assemble individuals into groups.

Key Contributions

• Spin glass self-assembly model: Developed a framework where opinions are represented as multidimensional spins that dynamically self-assemble into groups based on intragroup homophily and intergroup heterophily
• Phase diagram characterization: Computed the nontrivial phase diagram by solving self-consistency equations for “magnetization” (combined average opinion), revealing first-order transitions
• Empirical validation: Analytically derived group-size distributions that successfully match empirical data from online communities (Pardus massive multiplayer game)

Methodology

The approach combines statistical physics with social dynamics:

1. Group Hamiltonian: Define social stress as an energy function where individuals within a group share similar opinions (homophily) while opinions between groups tend to differ (heterophily)

2. Self-Assembly Theory: Apply canonical ensemble thermodynamics with corrections for structure formation statistics to derive equilibrium group-size distributions

3. Mean-Field Approximation: Derive self-consistency equations for average group opinion (magnetization) as a function of temperature (willingness to change opinions or groups)

4. Monte Carlo Simulations: Validate analytical predictions using Metropolis algorithm simulations with spin updates and group membership changes

Results

Below a critical (binodal) temperature, two stable phases coexist: an ordered phase with nonzero magnetization and large clusters, and a disordered phase with zero magnetization and no clusters. The system exhibits a first-order transition where large groups disintegrate above the critical temperature. The theoretical group-size distribution matches the Pardus online game data almost perfectly, with both showing Gini coefficients (G ≈ 0.90) near the percolation transition point.

Technologies

• Statistical Physics
• Spin Glass Theory
• Monte Carlo Simulations
• Self-Assembly Thermodynamics
• Network Analysis

(Korbel et al., 2023; Korbel et al., 2021)