  Signed graphs encode similarity and dissimilarity relationships among
different entities with positive and negative edges. In this paper, we study
the problem of community recovery over signed graphs generated by the signed
stochastic block model (SSBM) with two equal-sized communities. Our approach is
based on the maximum likelihood estimation (MLE) of the SSBM. Unlike many
existing approaches, our formulation reveals that the positive and negative
edges of a signed graph should be treated unequally. We then propose a simple
two-stage iterative algorithm for solving the regularized MLE. It is shown that
in the logarithmic degree regime, the proposed algorithm can exactly recover
the underlying communities in nearly-linear time at the information-theoretic
limit. Numerical results on both synthetic and real data are reported to
validate and complement our theoretical developments and demonstrate the
efficacy of the proposed method.
