  The task of community detection, which aims to partition a network into
clusters of nodes to summarize its large-scale structure, has spawned the
development of many competing algorithms with varying objectives. Some
community detection methods are inferential, explicitly deriving the clustering
objective through a probabilistic generative model, while other methods are
descriptive, dividing a network according to an objective motivated by a
particular application, making it challenging to compare these methods on the
same scale. Here we present a solution to this problem that associates any
community detection objective, inferential or descriptive, with its
corresponding implicit network generative model. This allows us to compute the
description length of a network and its partition under arbitrary objectives,
providing a principled measure to compare the performance of different
algorithms without the need for "ground truth" labels. Our approach also gives
access to instances of the community detection problem that are optimal to any
given algorithm, and in this way reveals intrinsic biases in popular
descriptive methods, explaining their tendency to overfit. Using our framework,
we compare a number of community detection methods on artificial networks, and
on a corpus of over 500 structurally diverse empirical networks. We find that
more expressive community detection methods exhibit consistently superior
compression performance on structured data instances, without having degraded
performance on a minority of situations where more specialized algorithms
perform optimally. Our results undermine the implications of the "no free
lunch" theorem for community detection, both conceptually and in practice,
since it is confined to unstructured data instances, unlike relevant community
detection problems which are structured by requirement.
