Social groups and social network formation

We present a dynamic model of social network formation in which a fixed number of agents interact in overlapping social groups. We derive several results on the formation of links in such networks, including results on the degree distribution, on comparative statics relating degree and group size, and on the dynamics of homophily. In particular, we derive comparative statics showing that degree is typically positively related to social group size but negatively related to the size of the overlap across multiple social groups. This is supported by evidence from a Facebook dataset. We also show that homophily over an agent's lifespan in the network can be non-monotonic, reaching a global maximum in some period before eventually decreasing.