  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 Oja's 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 Oja's algorithm, and work on asynchronous and gossip-type
algorithms for distributed computation.
