We give a simple distributed algorithm for computing adjacency matrix eigenvectors for the communication graph in an asynchronous gossip model. We show how to use this algorithm to give state-of-the-art asynchronous community detection algorithms when the communication graph is drawn from the well-studied stochastic block model. Our methods also apply to a natural alternative model of randomized communication, where nodes within a community communicate more frequently than nodes in different communities. Our analysis simplifies and generalizes prior work by forging a connection between asynchronous eigenvector computation and Ojas algorithm for streaming principal component analysis. We hope that our work serves as a starting point for building further connections between the analysis of stochastic iterative methods, like Ojas algorithm, and work on asynchronous and gossip-type algorithms for distributed computation.
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