We propose a new community detection approach to utilize the dependence of network connectivity. One of the most popular probabilistic models for fitting community structure is the stochastic block model (SBM). However, the SBM is not able to fully capture the dependence among edges from the same community. Various SBM approaches using the random effects are proposed to incorporate correlation among edges. However, this mainly designs for the exchangeable dependence structure. In this talk, we illustrate to approximate the true likelihood using the Bahadur representation which allows us to utilize the correlation information among edges within communities. The proposed method provides greater flexibility in handling different types of within-community dependence structure. In addition, the proposed algorithm does not involve specifying the likelihood function which could be intractable in community detection. This is joint work with Yubai Yuan.