Systematic assessment of the quality of fit of the stochastic block model for empirical networks
This work addresses the model selection problem for network scientists by assessing when SBM is sufficient, though it is incremental as it builds on existing methods.
The researchers systematically evaluated the fit of the stochastic block model (SBM) on 275 empirical networks, finding it accurately describes most networks but fails for those with large diameters and slow-mixing random walks, while it can handle high triangle abundance in many cases.
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.