Consistency of the maximum likelihood and variational estimators in a dynamic stochastic block model (Q2008607)

The stochastic block model (SBM) was introduced in [\textit{P. W. Holland} et al., ``Stochastic blockmodels: first steps'', Soc. Netw. 5, 109--137 (1983; \url{doi:10.1016/0378-8733(83)90021-7})]. This is the conventional graph model in which the nodes are partitioned into classes, where nodes' class memberships are represented by latent variables and the connection between two nodes. The present paper deals with the dynamic extension of the SBM graph model. The results are particularly interesting in connection with time-evolving networks (like global ionospheric maps of the total electron content) modeling taking into account the evolutionary behaviour of the random graphs. The nonstationary case (when the connectivity parameters are allowed to vary) is also considered.