Mixed preferential attachment model: Homophily and minorities in social networks

Individuals in social networks tend to exhibit homophily in their social ties, namely, they prefer bonding with others of the same social group (e.g., the same nationality, gender, socio-economic background, etc.). To formalize this phenomenon in the context of an evolving social network, we consider a mixed preferential attachment (MPA), bi-populated, network model. In this model each of the two social groups has a certain level of bias applied by its members toward other group members, ranging form homophily (affinity toward the same) to heterophily (affinity toward the different). Thus, the MPA model supports the following three simple and well-accepted observations on human behavior related to forming networks: (i) the “rich get richer” mechanism, (ii) heterogeneity and a resulting minority–majority partition, and (iii) selection bias between groups.