Two ways of comparing different SBM parametrisations in a statistically meaningful way are used: maximising the posterior likelihood and sampling across the posterior likelihood distribution. Both allow to establish the significance of the results by calculating the likelihood ratio for two candidate models. The first maximises the posterior likelihood of a given model and its parameters by applying the information theoretic Minimum Description Length (MDL) criterion . In minimising the description length, Σ, the posterior likelihood is maximised and, in effect, Occam's razor is implemented: The simplest model out of all models of equivalent explanatory power is preferred as it chooses the model that most compresses the data thus preventing overfitting . Using this approach the most probable partition could be found for each version of the stochastic block model and the obtained minimum description lengths (MDLs) could be compared. Since the model with the minimum description length is the most efficient representation of the data Σ allows for a principled way to carry out model selection and to discriminate between two alternative models.