In this work, we explore the state-space formulation of network processes to recover the underlying structure of the network (local connections). To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology inference problem. This approach provides a unified view of the traditional network control theory and signal processing on networks. In addition, it provides theoretical guarantees for the recovery of the topological structure of a deterministic linear dynamical system from input-output observations even though the input and state evolution networks can be different.