Stochastic Network Formation and Homophily

This chapter surveys and synthesizes models of network formation based on random graphs and stochastic processes. The material is organized according to whether the population is treated as fixed or evolving. Fixed population models allow one to readily capture a range of network properties through random graphs. Evolving population models allow one to study how network properties emerge asymptotically as a system grows according to some local rules. The chapter then turns to dynamic frameworks including search and matching, and structural models. The chapter pays particular attention to the effects of homophilous linking on network structure. Finally, the chapter discusses empirical and econometric issues based on stochastic network formation models.