Spatially high resolved neurophysiological data commonly pose a computational and analytical problem for the identification of functional networks in the human brain. We introduce a multivariate linear Granger Causality approach with an embedded dimension reduction that enables the computation of brain networks at the large scale. In order to grasp the information about connectivity patterns contained in the resulting high-dimensional directed networks, we furthermore propose the inclusion of module detection methods from network theory that can help to identify functionally associated brain areas. As a proof of concept, the methodology is verified by means of synthetic data with known ground truth module properties. Resting state fMRI data are used to demonstrate the applicability and benefit in the case of clinical data.