Whole-brain connectome data characterize the connections among distributed neural populations as a set of edges in a large network, and neuroscience research aims to systematically investigate associations between brain connectome and clinical or experimental conditions as covariates. A covariate is often related to a number of edges connecting multiple brain areas in an organized structure. However, in practice, neither the covariate-related edges nor the structure is known. Therefore, the understanding of underlying neural mechanisms relies on statistical methods that are capable of simultaneously identifying covariate-related connections and recognizing their network topological structures. The task can be challenging because of false-positive noise and almost infinite possibilities of edges combining into subnetworks. To address these challenges, we propose a new statistical approach to handle multivariate edge variables as outcomes and output covariate-related subnetworks. We first study the graph properties of covariate-related subnetworks from a graph and combinatorics perspective and accordingly bridge the inference for individual connectome edges and covariate-related subnetworks. Next, we develop efficient algorithms to exact covariate-related subnetworks from the whole-brain connectome data with an ℓ0 norm penalty. We validate the proposed methods based on an extensive simulation study, and we benchmark our performance against existing methods. Using our proposed method, we analyze two separate resting-state functional magnetic resonance imaging data sets for schizophrenia research and obtain highly replicable disease-related subnetworks
