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In this article, we advance divide-and-conquer strategies for solving thecommunity detection problem in networks. We propose two algorithms whichperform clustering on a number of small subgraphs and finally patches theresults into a single clustering. The main advantage of these algorithms isthat they bring down significantly the computational cost of traditionalalgorithms, including spectral clustering, semi-definite programs, modularitybased methods, likelihood based methods etc., without losing on accuracy andeven improving accuracy at times. These algorithms are also, by nature,parallelizable. Thus, exploiting the facts that most traditional algorithms areaccurate and the corresponding optimization problems are much simpler in smallproblems, our divide-and-conquer methods provide an omnibus recipe for scalingtraditional algorithms up to large networks. We prove consistency of thesealgorithms under various subgraph selection procedures and perform extensivesimulations and real-data analysis to understand the advantages of thedivide-and-conquer approach in various settings.

Two provably consistent divide and conquer clustering algorithms for large networks