Abstract: "Rich-get-richer" and "homophily" are two essential phenomena in evolving social networks. "Rich-get-richer" means people with greater followings are more likely to attract new followers, and "homophily" means people prefer to bond with others of the same social group, or who have some other attribute in common. To formalize these phenomena simultaneously in the context of an evolving social network, we consider a K-group preferential attachment (KPA) model, which is helpful for social network recommender systems. Our primary contribution is to propose a new evolving social network model that incorporates the mechanisms of rich-get-richer and homophily. We show that the proposed KPA model exhibits a power-law degree distribution for each group, and prove the central limit theorem for the maximum likelihood estimation of the parameters in the model. In addition, we verify the robustness of the proposed parameter estimation methods, and apply them to simulated data and to real-data examples.

Key words and phrases: Evolving network, homophily, preferential attachment, recommender system.