  In network analysis, within-community members are more likely to be connected
than between-community members, which is reflected in that the edges within a
community are intercorrelated. However, existing probabilistic models for
community detection such as the stochastic block model (SBM) are not designed
to capture the dependence among edges. In this paper, we propose a new
community detection approach to incorporate within-community dependence of
connectivities through the Bahadur representation. The proposed method does not
require specifying the likelihood function, which could be intractable for
correlated binary connectivities. In addition, the proposed method allows for
heterogeneity among edges between different communities. In theory, we show
that incorporating correlation information can lower estimation bias and
accelerate algorithm convergence. Our simulation studies show that the proposed
algorithm outperforms the popular variational EM algorithm assuming conditional
independence among edges. We also demonstrate the application of the proposed
method to agricultural product trading networks from different countries.
