  Community detection in large social networks is affected by degree
heterogeneity of nodes. The D-SCORE algorithm for directed networks was
introduced to reduce this effect by taking the element-wise ratios of the
singular vectors of the adjacency matrix before clustering. Meaningful results
were obtained for the statistician citation network, but rigorous analysis on
its performance was missing. First, this paper establishes theoretical
guarantee for this algorithm and its variants for the directed degree-corrected
block model (Directed-DCBM). Second, this paper provides significant
improvements for the original D-SCORE algorithms by attaching the nodes outside
of the community cores using the information of the original network instead of
the singular vectors.
