Stochastic blockmodels for directed graphs

Yuchung J. Wang, George Y. Wong

Research output: Contribution to journalArticlepeer-review

257 Scopus citations


Holland and Leinhardt (1981) proposed the p1model 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 p1model completely ignores this extra piece of information and is, therefore, unable to explain the block structure. Blockmodels that are simple extensions of the p1model 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.

Original languageEnglish (US)
Pages (from-to)8-19
Number of pages12
JournalJournal of the American Statistical Association
Issue number397
StatePublished - Mar 1987

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Blockmodeling technique
  • Iterative scaling algorithm
  • Stochastic partitioned directed graph


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