  The dynamics of systems of interacting agents is determined by the structure
of their coupling network. The knowledge of the latter is, therefore, highly
desirable, for instance, to develop efficient control schemes, to accurately
predict the dynamics, or to better understand inter-agent processes. In many
important and interesting situations, the network structure is not known,
however, and previous investigations have shown how it may be inferred from
complete measurement time series on each and every agent. These methods
implicitly presuppose that, even though the network is not known, all its nodes
are. Here, we investigate the different problem of inferring network structures
within the observed/measured agents. For symmetrically coupled dynamical
systems close to a stable equilibrium, we establish analytically and illustrate
numerically that velocity signal correlators encode not only direct couplings,
but also geodesic distances in the coupling network within the subset of
measurable agents. When dynamical data are accessible for all agents, our
method is furthermore algorithmically more efficient than the traditional ones
because it does not rely on matrix inversion.
