Scalable Community Detection in the Degree-Corrected Stochastic Block Model

Abstract

Community detection aims to partition a connected graph into a small number of clusters. The Degree-Corrected Stochastic Block Model (DCSBM) is one popular generative model that yields graphs with varying degree distributions within the communities. However, large computational complexity and storage requirements of existing approaches for DCSBM limit their scalability to large graphs. In this paper, we advance a scalable framework for DCSBM, in which the full graph is first sub-sampled by selecting a small subset of the nodes, then a clustering of the induced subgraph is obtained, followed by low-complexity retrieval of the global community structure from the clustering of the graph sketch. To sample the underlying graph, we introduce a family of sampling schemes that capture local community structures using metrics derived from the average neighbor degrees, which are shown to achieve the twin objective of sampling from low-density clusters and identifying high-degree nodes within each cluster. The proposed approach can perform on par with full scale clustering while affording substantial complexity and storage gains as demonstrated through experiments using both synthetic and real data.