High dimensional functional MRI data in combination with a low temporal resolution imposes computational limits on classical Granger Causality analyses with respect to a large-scale representations of functional interactions in the brain. To overcome these limitations and exploit information inherent in resulting brain connectivity networks at the large scale, we propose a multivariate Granger Causality approach with embedded dimension reduction. Using this approach, we computed binary connectivity networks from resting state fMRI images and analyzed them with respect to network module structure, which might be linked to distinct brain regions with an increased density of particular interaction patterns as compared to inter-module regions. As a proof of concept, we show that the modular structure of these large-scale connectivity networks can be recovered. These results are promising since further analysis of large-scale brain network partitions into modules might prove valuable for understanding and tracing changes in brain connectivity at a more detailed resolution level than before.