  A principled approach to understand network structures is to formulate
generative models. Given a collection of models, however, an outstanding key
task is to determine which one provides a more accurate description of the
network at hand, discounting statistical fluctuations. This problem can be
approached using two principled criteria that at first may seem equivalent:
selecting the most plausible model in terms of its posterior probability; or
selecting the model with the highest predictive performance in terms of
identifying missing links. Here we show that while these two approaches yield
consistent results in most of cases, there are also notable instances where
they do not, that is, where the most plausible model is not the most
predictive. We show that in the latter case the improvement of predictive
performance can in fact lead to overfitting both in artificial and empirical
settings. Furthermore, we show that, in general, the predictive performance is
higher when we average over collections of models that are individually less
plausible, than when we consider only the single most plausible model.
