In this note, we consider networks that are governed by external controls. The internal nodes of the network are composed of structured linear dynamic systems with a single incoming state vertex and a single outgoing state vertex. Combining the network graph with the node graphs provides with a global graph that will allow the study of the structural controllability of the global system. We give necessary and sufficient controllability conditions for the global system, with respect to the controllability of the nodes and to the properties of the network graph. The conditions are expressed in terms of an auxiliary graph that has the same size as the network graph, but takes into account important features of the node graphs. Besides its interest in terms of insight in the controllability of networks with dynamical nodes, this approach is also much more efficient computationally than a direct checking of the controllability of the global system.