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This paper deals with identifiability of undirected dynamical networks withsingle-integrator node dynamics. We assume that the graph structure of suchnetworks is known, and aim to find graph-theoretic conditions under which thestate matrix of the network can be uniquely identified. As our maincontribution, we present a graph coloring condition that ensuresidentifiability of the network's state matrix. Additionally, we show how theframework can be used to assess identifiability of dynamical networks withgeneral, higher-order node dynamics. As an interesting corollary of ourresults, we find that excitation and measurement of all network nodes is notrequired. In fact, for many network structures, identification is possible withonly small fractions of measured and excited nodes.

Identifiability of Undirected Dynamical Networks: a Graph-Theoretic Approach