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On the problem of reconstructing an unknown topology

The interest for networks of dynamical systems has been increasing in the past years, especially because of their capability of modeling and describing a large variety of phenomena and behaviors. Particular attention has been oriented towards the emergence of complicated phenomena from interconnections of simple models. In this paper we tackle, from a theoretical perspective, the problem of reconstructing the topology of an unknown network of dynamical systems. We propose a technique, based on Wiener filtering, which provides general theoretical guarantees for the detection of links in a network of dynamical systems. For a large class of network that we name “self-kin” sufficient conditions for a correct detection of a link are formulated. For networks not belonging to this class we give conditions for correct detection of links belonging to the smallest self-kin network containing the actual one.