  We present new results on community recovery based on the PageRank Nibble
algorithm on a sparse directed stochastic block model (dSBM). Our results are
based on a characterization of the local weak limit of the dSBM and the
limiting PageRank distribution. This characterization allows us to estimate the
probability of misclassification for any given connection kernel and any given
number of seeds (vertices whose community label is known). The fact that
PageRank is a local algorithm that can be efficiently computed in both a
distributed and asynchronous fashion, makes it an appealing method for
identifying members of a given community in very large networks where the
identity of some vertices is known.
