A Characterization of the Modular Structure of Complex Networks Based on Consensual Communities

Understanding the community structure in graphs arising from complex network is an important and difficult problem, both from theoretical and practical points of views. Although a lot of community detection algorithms have been proposed in the last decade, there is still no satisfactory way to determine if a given network possesses or not a community structure, that is, its nodes can be partitioned in well separated clusters. In this paper, we propose a new criterion based on the study of the formation of consensual communities obtained by running several times a non deterministic algorithm. By testing on synthetic benchmarks (with known structure) and on several real world networks, we show that the graphs can be categorized in several classes according to the dynamic of the consensual communities formation process. This result is promising to derive new approaches to characterize the modular structure of graphs.