Does ‘Community Detection’ Find Real Emerging Meso-structures? A Statistical Test Based on Complex Networks Methods

Multiple systems that can be represented in network terms usually present areas where the nodes are densely connected among themselves. Community detection analysis is precisely pointing at revealing these areas, thus providing a partition of the network under investigation. Usually, the results of such analysis are discussed in descriptive terms, either with the aid of some statistics, or by listing and discussing the nodes that belong to the different communities. Thus, a statistical evaluation of the detected community structure still missing in literature. In this work, we design a series of tests to assess if the community detection results are compatible with random processes of tie formation, or if what emerges from such analysis cannot be ascribable to randomness. As community detection naturally points at uncovering the presence of meso-structures within a system, what needed is a statistical tool to test if these are just areas that have randomly formed or if, behind what is detected, there is a real emerging phenomenon. In order to provide an example, we run the tests on the network of UK Faculty and discuss the results.