  A nonparametric approach to the modeling of social networks using
degree-corrected stochastic blockmodels is proposed. The model for static
network consists of a stochastic blockmodel using a probit regression
formulation and popularity parameters are incorporated to account for degree
heterogeneity. Dirichlet processes are used to detect community structure as
well as induce clustering in the popularity parameters. This approach is
flexible yet parsimonious as it allows the appropriate number of communities
and popularity clusters to be determined automatically by the data. We further
discuss some ways of extending the static model to dynamic networks. We
consider a Bayesian approach and derive Gibbs samplers for posterior inference.
The models are illustrated using several real-world benchmark social networks.
