Exact Recovery Discrimination in Planted Bisection Model

Community detection is one of the core issues in the statistical analysis of network data. In this paper, we study a sufficient condition under which the community structure can be exactly recovered with high probability in the sparse asymmetric planted bisection models. Using the idea of the maximum likelihood method, we obtain a threshold, which is only related to the probabilities of edge presence in the denser community and between communities, for the community detection in the proposed model. In addition, we conduct a series of simulation studies to demonstrate our theoretical results with the spectral clustering method.