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.
In REF , Tumminello et al. proposed a statistical method to characterize the communities in terms of the over-expressed attributes found in the elements of the community.
Community characterization of heterogeneous complex systems
J. Stat. Mech., P01019, (2011)
Physics Computer Science Mathematics