Spectral embedding of adjacency or Laplacian matrices of undirected graphs isa common technique for representing a network in a lower dimensional latentspace, with optimal theoretical guarantees. The embedding can be used toestimate the community structure of the network, with strong consistencyresults in the stochastic blockmodel framework. One of the main practicallimitations of standard algorithms for community detection from spectralembeddings is that the number of communities and the latent dimension of theembedding must be specified in advance. In this article, a novel Bayesian modelfor simultaneous and automatic selection of the appropriate dimension of thelatent space and the number of blocks is proposed. Extensions to directed andbipartite graphs are discussed. The model is tested on simulated and real worldnetwork data, showing promising performance for recovering latent communitystructure.
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