Identifying Well-Connected Communities in Real-World and Synthetic Networks

Minhyuk Park, Yasamin Tabatabaee, Vikram Ramavarapu, Baqiao Liu, Vidya Kamath Pailodi, Rajiv Ramachandran, Dmitriy Korobskiy, Fábio Ayres, George Chacko, Tandy J. Warnow

Abstract: Integral to the problem of detecting communities through graph clustering is the expectation that they are “well-connected”. Surprisingly, we find that the output of multiple clustering approaches–the Leiden algorithm with either the Constant Potts Model or modularity as quality function, Iterative K-Core Clustering, Infomap, and Markov Clustering–include communities that fail even a mild requirement for well-connectedness. As a remediation strategy, we have developed the “Connectivity Modifier” (CM), which iteratively removes small edge cuts and re-clusters until all communities detected are well-connected. Results from real-world networks with up to 75,025,194 nodes illustrate how CM enables additional insights into community structure within networks, while results on synthetic networks show that the CM algorithm improves accuracy in recovering true communities. Our study also raises questions about the “clusterability” of networks and mathematical models of community structure.