  We introduce an analytical statistical method to characterize the communities
detected in heterogeneous complex systems. By posing a suitable null
hypothesis, our method makes use of the hypergeometric distribution to assess
the probability that a given property is over-expressed in the elements of a
community with respect to all the elements of the investigated set. We apply
our method to two specific complex networks, namely a network of world movies
and a network of physics preprints. The characterization of the elements and of
the communities is done in terms of languages and countries for the movie
network and of journals and subject categories for papers. We find that our
method is able to characterize clearly the identified communities. Moreover our
method works well both for large and for small communities.
