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The dynamics of systems of interacting agents is determined by the structureof their coupling network. The knowledge of the latter is, therefore, highlydesirable, for instance, to develop efficient control schemes, to accuratelypredict the dynamics, or to better understand inter-agent processes. In manyimportant and interesting situations, the network structure is not known,however, and previous investigations have shown how it may be inferred fromcomplete measurement time series on each and every agent. These methodsimplicitly presuppose that, even though the network is not known, all its nodesare. Here, we investigate the different problem of inferring network structureswithin the observed/measured agents. For symmetrically coupled dynamicalsystems close to a stable equilibrium, we establish analytically and illustratenumerically that velocity signal correlators encode not only direct couplings,but also geodesic distances in the coupling network within the subset ofmeasurable agents. When dynamical data are accessible for all agents, ourmethod is furthermore algorithmically more efficient than the traditional onesbecause it does not rely on matrix inversion.

Reconstructing Network Structures from Partial Measurements