Well-connectedness and community detection

Community detection methods help reveal the meso-scale structure of complex networks. Integral to detecting communities is the expectation that communities in a network are edge-dense and “well-connected”. Surprisingly, we find that five different community detection methods–the Leiden algorithm optimizing the Constant Potts Model, the Leiden algorithm optimizing modularity, Infomap, Markov Cluster (MCL), and Iterative k-core (IKC)–identify communities that fail even a mild requirement for well-connectedness. To address this issue, we have developed the Connectivity Modifier (CM), which iteratively removes small edge cuts and re-clusters until communities are well-connected according to a user-specified criterion. We tested CM on real-world networks ranging in size from approximately 35,000 to 75,000,000 nodes. Post-processing of the output of community detection methods by CM resulted in a reduction in node coverage. Results on synthetic networks show that the CM algorithm generally maintains or improves accuracy in recovering true communities. This study underscores the importance of network clusterability–the fraction of a network that exhibits community structure–and the need for more models of community structure where networks contain nodes that are not assigned to communities. In summary, we address well-connectedness as an important aspect of clustering and present a scalable open-source tool for well-connected clusters.