  Spectral embedding of adjacency or Laplacian matrices of undirected graphs is
a common technique for representing a network in a lower dimensional latent
space, with optimal theoretical guarantees. The embedding can be used to
estimate the community structure of the network, with strong consistency
results in the stochastic blockmodel framework. One of the main practical
limitations of standard algorithms for community detection from spectral
embeddings is that the number of communities and the latent dimension of the
embedding must be specified in advance. In this article, a novel Bayesian model
for simultaneous and automatic selection of the appropriate dimension of the
latent space and the number of blocks is proposed. Extensions to directed and
bipartite graphs are discussed. The model is tested on simulated and real world
network data, showing promising performance for recovering latent community
structure.
