Stochastic Blockmodels for Directed Graphs

Abstract Holland and Leinhardt (1981) proposed the p 1 model for the analysis of binary directed graph data in network studies. Such a model provides information about the “attractiveness” and “expansiveness” of the individual nodes in the network, as well as the tendency of a pair of nodes to reciprocate relational ties. When the nodes are a priori partitioned into subgroups based on attributes such as race and sex, the density of ties from one subgroup to another can differ considerably from that relating another pair of subgroups, thus creating a situation called blocking in social networks. The p 1 model completely ignores this extra piece of information and is, therefore, unable to explain the block structure. Blockmodels that are simple extensions of the p 1 model are proposed specifically for such data. An iterative scaling algorithm is presented for fitting the model parameters by maximum likelihood. The methodology is illustrated in detail on two empirical examples.