Learning influence pathways of a network of dynamically related processes\nfrom observations is of considerable importance in many disciplines. In this\narticle, influence networks of agents which interact dynamically via linear\ndependencies are considered. An algorithm for the reconstruction of the\ntopology of interaction based on multivariate Wiener filtering is analyzed. It\nis shown that for a vast and important class of interactions, that respect flow\nconservation, the topology of the interactions can be exactly recovered. The\nclass of problems where reconstruction is guaranteed to be exact includes power\ndistribution networks, dynamic thermal networks and consensus networks. The\nefficacy of the approach is illustrated through simulation and experiments on\nconsensus networks, IEEE power distribution networks and thermal dynamics of\nbuildings.\n