  Community detection is a fundamental statistical problem in network data
analysis. Many algorithms have been proposed to tackle this problem. Most of
these algorithms are not guaranteed to achieve the statistical optimality of
the problem, while procedures that achieve information theoretic limits for
general parameter spaces are not computationally tractable. In this paper, we
present a computationally feasible two-stage method that achieves optimal
statistical performance in misclassification proportion for stochastic block
model under weak regularity conditions. Our two-stage procedure consists of a
generic refinement step that can take a wide range of weakly consistent
community detection procedures as initializer, to which the refinement stage
applies and outputs a community assignment achieving optimal misclassification
proportion with high probability. The practical effectiveness of the new
algorithm is demonstrated by competitive numerical results.
