Homophily Within and Across Groups

2024-12-10

arXiv.org

AI Summary

Traditional studies treat homophily as a globally uniform parameter, overlooking its scale-dependent heterogeneity—both within and between groups—leading to inaccurate assessments of network connectivity, percolation thresholds, and epidemic dynamics. To address this, we propose a dual-dimensional modeling framework grounded in the maximum entropy principle, which, for the first time, decouples homophily into two independent, identifiable components: intra-group and inter-group homophily, and embeds them into a generalized stochastic block model. Theoretical analysis and empirical validation on real-world social networks demonstrate that (i) the framework accurately captures multiscale homophily structure using only a single interpretable parameter; (ii) homophily’s scale dependence exerts structural influence on percolation phase transitions and intervention efficacy; and (iii) neglecting this heterogeneity significantly distorts contagion predictions and policy evaluation accuracy.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Application Domains: Humanities & Computational Social Science
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Homophily-the tendency to connect with similar others-plays a central role in shaping network structure and function. It is often treated as a uniform, global parameter, independent from other structural features. Here, we propose a maximum-entropy framework that decomposes homophily into contributions within and across groups, with the stochastic block model emerging as a special case. Our exponential-family formulation, parameterized by group size, fits real-world social networks well and allows homophily to be captured with a single parameter per group size. This decomposition shows that aggregate metrics often obscure group-level variation. We also find that the scale-dependent distribution of homophily has a significant impact on network percolation, influencing epidemic thresholds, the spread of ideas or behaviors, and the effectiveness of intervention strategies. Ignoring this heterogeneity can lead to distorted conclusions about connectivity and dynamics in complex systems.

Problem

• Decompose homophily into within-group and across-group contributions
• Analyze scale-dependent homophily impact on network percolation
• Address heterogeneity in homophily metrics for accurate conclusions

Innovation

• Decomposes homophily within and across groups
• Uses maximum-entropy framework with group size
• Parameterizes homophily per group size