Incorporating Homophily into Growth-Based Network Models: A Computational Framework

Homophily, the principle that similarity breeds connection, shapes network formation across diverse social systems, from scientific collaborations to online communities. While this phenomenon profoundly influences how information flows, how communities form, and how opportunities distribute within networks, classical growth-based models typically lack general mechanisms for incorporating it. This paper presents a computational framework that bridges this gap. Through a retry-based wrapper algorithm, we augment any growth-based network model with homophilic bias while preserving its original selection mechanisms. The framework remains agnostic to both the underlying growth model and the similarity function, requiring only a measure of node similarity. Its efficiency is guaranteed through bounded retry counts, making it practical for large-scale network generation. Validation using the Barabási-Albert and Holme-Kim models demonstrates successful incorporation of statistically significant homophilic patterns. In our experiments, these variants preserved their characteristic properties - power-law distributions for both models and clustering coefficients for Holme-Kim. The extended Holme-Kim model is particularly valuable for social network research, combining scale-free topology, high clustering, and homophilic attachment. The framework provides a systematic method for incorporating arbitrary bias functions into network models, advancing our ability to study complex social systems computationally.