Dynamic degree-corrected blockmodels for social networks: a nonparametric approach

Abstract

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.