A Markov chain analysis of the dynamics of homophily

Many networks are made up of different nodes types, which are determined by a set of common quantitative or qualitative node properties. Understanding the effects of homophilic relationships, that is, the tendency of nodes to establish links to other nodes that are alike, requires formal frameworks that explain how local decision-making mechanisms contribute to the formation of particular network structures. Based on two simple stochastic mechanisms for establishing links, this article introduces a model that explains the emergence of homophily as an aggregate group and network level outcome. We characterize the dynamics of homophily and present conditions that guarantee that the amount of homophily exceeds the expected amount of a purely random decision-making process. Moreover, we show that the proposed model resembles patterns of homophily in a citation network of political blogs. Finally, we use the model to design a non-homophilic node detection algorithm for identifying nodes that establish connections without a particular preference for either node type.