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We give a simple distributed algorithm for computing adjacency matrixeigenvectors for the communication graph in an asynchronous gossip model. Weshow how to use this algorithm to give state-of-the-art asynchronous communitydetection algorithms when the communication graph is drawn from thewell-studied stochastic block model. Our methods also apply to a naturalalternative model of randomized communication, where nodes within a communitycommunicate more frequently than nodes in different communities. Our analysissimplifies and generalizes prior work by forging a connection betweenasynchronous eigenvector computation and Oja's algorithm for streamingprincipal component analysis. We hope that our work serves as a starting pointfor building further connections between the analysis of stochastic iterativemethods, like Oja's algorithm, and work on asynchronous and gossip-typealgorithms for distributed computation.

Eigenvector Computation and Community Detection in Asynchronous Gossip Models