Fast Community Detection with Graph Sparsification

A popular model for detecting community structure in large graphs is the Stochastic Block Model (SBM). The exact parameters to recover the community structure of a SBM has been well studied, and many methods have been proposed to recover a nodes’ community membership. A popular approach is to use spectral methods where the Graph Laplacian L of the given graph is created, and the Fiedler vector of the graph is found. This vector is then used to cluster nodes in the same community. While a robust method, it can be expensive to compute the Fiedler vector exactly. In this paper we examine the types of errors that can be tolerated using spectral methods while still recovering the communities. The two sources of error considered are: (i) dropping edges using different sparsification strategies; and (ii) inaccurately computing the eigenvectors. In this way, spectral clustering algorithms can be tuned to be far more efficient at detecting community structure for these community models.