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We perform a systematic analysis of the quality of fit of the stochasticblock model (SBM) for 275 empirical networks spanning a wide range of domainsand orders of size magnitude. We employ posterior predictive model checking asa criterion to assess the quality of fit, which involves comparing networksgenerated by the inferred model with the empirical network, according to a setof network descriptors. We observe that the SBM is capable of providing anaccurate description for the majority of networks considered, but falls shortof saturating all modeling requirements. In particular, networks possessing alarge diameter and slow-mixing random walks tend to be badly described by theSBM. However, contrary to what is often assumed, networks with a high abundanceof triangles can be well described by the SBM in many cases. We demonstratethat simple network descriptors can be used to evaluate whether or not the SBMcan provide a sufficiently accurate representation, potentially pointing topossible model extensions that can systematically improve the expressiveness ofthis class of models.

Systematic assessment of the quality of fit of the stochastic block model for empirical networks