  We perform a systematic analysis of the quality of fit of the stochastic
block model (SBM) for 275 empirical networks spanning a wide range of domains
and orders of size magnitude. We employ posterior predictive model checking as
a criterion to assess the quality of fit, which involves comparing networks
generated by the inferred model with the empirical network, according to a set
of network descriptors. We observe that the SBM is capable of providing an
accurate description for the majority of networks considered, but falls short
of saturating all modeling requirements. In particular, networks possessing a
large diameter and slow-mixing random walks tend to be badly described by the
SBM. However, contrary to what is often assumed, networks with a high abundance
of triangles can be well described by the SBM in many cases. We demonstrate
that simple network descriptors can be used to evaluate whether or not the SBM
can provide a sufficiently accurate representation, potentially pointing to
possible model extensions that can systematically improve the expressiveness of
this class of models.
