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In this article, we explore the state-space formulation of a network process to recover from partial observations the network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system identification literature and extend them to the network topology identification problem. This approach provides a unified view of network control and signal processing on graphs. In addition, we provide theoretical guarantees for the recovery of the topological structure of a deterministic continuous-time linear dynamical system from input-output observations even when the input and state interaction networks are different. Our mathematical analysis is accompanied by an algorithm for identifying from data,a network topology consistent with the system dynamics and conforms to the prior information about the underlying structure. The proposed algorithm relies on alternating projections and is provably convergent. Numerical results corroborate the theoretical findings and the applicability of the proposed algorithm.
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