Multivariate Granger Causality (MVGC) approaches have recently been employed to estimate the directionality of brain connectivity. While BOLD fluctuations also contain information about neurovascular coupling, so far all MVGC estimation frameworks have focused on central tendencies, hence disregarding directed coupling between volatilities (i.e. in-variance causality). In this paper, we develop a framework for simultaneous estimation of both in-mean and in-variance causality in complex networks. We validate our approach using synthetic data from complex ensembles of coupled nonlinear oscillators, and successively employ HCP data to provide the very first estimate of the in-variance connectome of the human brain.