An empirical characterization of community structures in complex networks using a bivariate map of quality metrics

Community detection emerges as an important task in the discovery of network mesoscopic structures. However, the concept of a "good" community is very context-dependent and it is relatively complicated to deduce community characteristics using available community detection techniques. In reality, the existence of a gap between structural goodness quality metrics and expected topological patterns creates a confusion in evaluating community structures. In this paper, we introduce an empirical multivariate analysis of different structural goodness properties in order to characterize several detectable community topologies. Specifically, we show that a combination of two representative structural dimensions including community transitivity and hub dominance allows to distinguish different topologies such as star-based, clique-based, string-based and grid-based structures. Additionally, these classes of topology disclose structural proximities with those of graphs created by Erd\H{o}s-R\'{e}nyi, Watts-Strogatz and Barab\'{a}si-Albert generative models. We illustrate popular community topologies identified by different detection methods on a large dataset composing many network categories and associate their structures with the most related graph generative model. Interestingly, this conjunctive representation sheds light on fundamental differences between mesoscopic structures in various network categories including: communication, information, biological, technological, social, ecological, synthetic networks and more.