Statistically optimal graph partition method based on modularity

Graph theory provides a formal framework to investigate the functional and structural connectome of the brain. We extend previous work on modularity-based graph partitioning methods that are able to detect network community structures. We estimate the conditional expected network, provide exact analytical solutions for a Gaussian random network, and also demonstrate that this network is the best unbiased linear estimator even when the Gaussian assumption is violated. We use the conditional expected network to partition graphs, and demonstrate its performance in simulations, a real network dataset, and a structural brain connectivity network.