Exact Recovery Discrimination in Planted Bisection Models

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 or not in the sparse asymmetric planted bisection models. Using 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.