  We conduct a comparative analysis on various estimates of the number of
clusters in community detection. An exhaustive comparison requires testing of
all possible combinations of frameworks, algorithms, and assessment criteria.
In this paper we focus on the framework based on a stochastic block model, and
investigate the performance of greedy algorithms, statistical inference, and
spectral methods. For the assessment criteria, we consider modularity, map
equation, Bethe free energy, prediction errors, and isolated eigenvalues. From
the analysis, the tendency of overfit and underfit that the assessment criteria
and algorithms have, becomes apparent. In addition, we propose that the
alluvial diagram is a suitable tool to visualize statistical inference results
and can be useful to determine the number of clusters.
