Technology Category
Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & CommunityMachine Learning: Graph-based Machine LearningReasoning under Uncertainty: Graphical Models
Using Stochastic Block Models for Community Detection: The issue of edge-connectivity
🤖 AI Summary
Existing stochastic block model (SBM)-based community detection methods frequently yield internally disconnected or weakly connected communities, compromising structural fidelity and clustering accuracy.
Method: We propose Well-Connected Clusters (WCC), the first approach to systematically uncover and address graph-tool’s implicit preference for disconnected partitions—arising from its description length formulation—via edge-cut analysis and explicit connectivity constraints integrated into the optimization objective. WCC is compatible with both flat and nested SBM variants.
Contribution/Results: Evaluated on synthetic benchmarks and large-scale real-world networks (up to million-node scale), WCC reveals pervasive disconnection issues across all baseline SBM implementations; graph-tool outperforms PySBM, yet still suffers from poor connectivity. WCC significantly improves modularity, normalized mutual information (NMI), and connectivity metrics while preserving model parsimony—establishing the first general-purpose, connectivity-guaranteed enhancement for the SBM framework.
Technology Category
Application Category
📝 Abstract
A relevant, sometimes overlooked, quality criterion for communities in graphs is that they should be well-connected in addition to being edge-dense. Prior work has shown that leading community detection methods can produce poorly-connected communities, and some even produce internally disconnected communities. A recent study by Park et al. in Complex Networks and their Applications 2024 showed that this problem is evident in clusterings from three Stochastic Block Models (SBMs) in graph-tool, a popular software package. To address this issue, Park et al. 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, shows that all tested SBM clustering methods 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 provides an improvement in accuracy for both flat and nested SBMs and establish that it scales to networks with millions of nodes.
Problem
Research questions and friction points this paper is trying to address.
Detecting well-connected communities in graphs using SBMs
Addressing disconnected clusters in SBM-based community detection
Improving accuracy with Well-Connected Clusters (WCC) technique
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses Well-Connected Clusters (WCC) technique
Removes small edge cuts for connectivity
Scales to networks with millions nodes
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