  Bipartite graphs are ubiquitous across various scientific and engineering
fields. Simultaneously grouping the two types of nodes in a bipartite graph via
biclustering represents a fundamental challenge in network analysis for such
graphs. The latent block model (LBM) is a commonly used model-based tool for
biclustering. However, the effectiveness of the LBM is often limited by the
influence of row and column sums in the data matrix. To address this
limitation, we introduce the degree-corrected latent block model (DC-LBM),
which accounts for the varying degrees in row and column clusters,
significantly enhancing performance on real-world data sets and simulated data.
We develop an efficient variational expectation-maximization algorithm by
creating closed-form solutions for parameter estimates in the M steps.
Furthermore, we prove the label consistency and the rate of convergence of the
variational estimator under the DC-LBM, allowing the expected graph density to
approach zero as long as the average expected degrees of rows and columns
approach infinity when the size of the graph increases.
