Abstract
We introduce an analytical statistical method for characterizing the communities detectedin heterogeneous complex systems. By proposing a suitable null hypothesis, our methodmakes use of the hypergeometric distribution to assess the probability that a givenproperty is over-expressed in the elements of a community with respect to all theelements of the investigated set. We apply our method to two specific complexnetworks, namely a network of world movies and a network of physics preprints.The characterization of the elements and of the communities is done in termsof languages and countries for the movie network and of journals and subjectcategories for papers. We find that our method is able to characterize clearly thecommunities identified. Moreover our method works well both for large and for smallcommunities.
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