Seeing as an exact evaluation of the model evidence is not tractable approximations have to be used which are implemented in graph-tool. Thus, during a first step the description length of the SBM is minimised to initialise the Markov chain. Subsequently 200,000 sweeps were carried out using graph-tool's MCMC algorithm to sample the posterior density, recording the description length at each step. At the end by subtracting the average description length from the entropy (calculated using the Bethe approximation) the model evidence can be evaluated . This was carried out for the configurations of the SBM recorded in Table . This algorithm was run three times for each configuration to find a mean and standard deviation. Seeing as the above method returns the log-likelihood, Λ 2 could be calculated by subtracting the two values for the two hypotheses being compared and raising the answer to the base of 𝑒.