Network representation of brain connectivity has provided a novel means of investigating brain changes arising from pathology, development or aging. The high dimensionality of these networks demands methods that are not only able to extract the patterns that highlight these sources of variation, but describe them individually. In this paper, we present a unified framework for learning subnetwork patterns of connectivity by their projective non-negative decomposition into a reconstructive basis set, as well as, additional basis sets representing development and group discrimination. In order to obtain these components, we exploit the geometrical distribution of the population in the connectivity space by using a graph-theoretical scheme that imposes locality-preserving properties. In addition, the projection of the subject networks into the basis set provides a low dimensional representation of it, that teases apart the different sources of variation in the sample, facilitating variation-specific statistical analysis. The proposed framework is applied to a study of diffusion-based connectivity in subjects with autism.