Using stochastic block models for community detection

Abstract A recent study reported by Park et al. (Improved community detection using stochastic block models, Springer, Heidelberg, 2025) in Complex Networks and their Applications 2024 showed that clusterings from three Stochastic Block Models (SBMs) in graph-tool, a popular software package, often had internally disconnected clusters when used on large real-world or synthetic networks. To address this issue, Park et al. (Improved community detection using stochastic block models, Springer, Heidelberg, 2025) presented a simple technique, Well-Connected Clusters (WCC), that repeatedly finds and removes small edge cuts of size at most $$\log _{10}n$$ in clusters, where n is the number of nodes in the cluster, and showed that treatment of graph-tool SBM clusterings with WCC improves accuracy. Here we examine the question of cluster connectivity for clusterings computed using other SBM software or nested SBMs within graph-tool. Our study, using a wide range of real-world and synthetic networks ranging up to more than a million nodes, shows that all tested SBM clustering methods frequently produce communities that are disconnected, and that graph-tool improves on PySBM. We provide insight into why graph-tool degree-corrected SBM clustering produces disconnected clusters by examining the description length formula it uses, and explore the impact of modifications to the description length formula. Finally, we show that WCC generally provides an improvement in accuracy for both flat and nested SBMs, except for cases where nearly all nodes in the network are in very sparse ground-truth clusters. We also demonstrate that WCC scales to networks with millions of nodes.