On the necessity of full-state measurement for state-space network reconstruction

Network reconstruction is an important research topic in many different applications, including biochemical reactions, critical infrastructures, social media, and wireless mesh networks. This paper shows that, for a certain important class of systems, all the states in a system must be measured in order to ensure correct reconstruction of the network. Furthermore, we show that this result is strongly necessary, in that if only one state is not measured, the structure of the recovered network could be arbitrarily different from the structure of the actual network. Finally, we note that our results motivate the need for dynamical structure functions, a partial structure system representation that reveals important structural information about the system but requires much less a priori information (than knowledge of full state measurements) for reconstruction from data.