Network neuroscience aims to understand the relationship between response, (e.g. IQ or depression) and connectome: measures of connectivity between many regions of interest (ROIs) in the brain. Typical practice vectorizes edge weights and applies standard statistical methods. However, connectomes are “network data objects,” and this approach fails to use structure to support prediction, interpretability, and inference. Beyond network structure, the ROIs that are nodes of the network can be annotated with standard brain coordinates, and much is known about the function of these ROIs and their hierarchical organization as communities. In addition, covariates associated with the ROIs can be leveraged. While statistical tasks in this domain are often formulated in terms of prediction, the goal is typically understanding. We present work focused on enhancing interpretability of predictive models through group sparsity, where the groups are specified a priori to respect the inherent structure of the data. We present numerical experiments to contrast our proposed methods with standard approaches and illustrate the utility of these new techniques on several human neuroimaging datasets.