  Inference for the stochastic blockmodel is currently of burgeoning interest
in the statistical community, as well as in various application domains as
diverse as social networks, citation networks, brain connectivity networks
(connectomics), etc. Recent theoretical developments have shown that spectral
embedding of graphs yields tractable distributional results; in particular, a
random dot product latent position graph formulation of the stochastic
blockmodel informs a mixture of normal distributions for the adjacency spectral
embedding. We employ this new theory to provide an empirical Bayes methodology
for estimation of block memberships of vertices in a random graph drawn from
the stochastic blockmodel, and demonstrate its practical utility. The posterior
inference is conducted using a Metropolis-within-Gibbs algorithm. The theory
and methods are illustrated through Monte Carlo simulation studies, both within
the stochastic blockmodel and beyond, and experimental results on a Wikipedia
data set are presented.
