This article studies the problem of reconstructing the topology of a network
of interacting agents via observations of the state-evolution of the agents. We
focus on the large-scale network setting with the additional constraint of
partial observations, where only a small fraction of the agents can be
feasibly observed. The goal is to infer the underlying subnetwork of
interactions and we refer to this problem as localtomography. In order to
study the large-scale setting, we adopt a proper stochastic formulation where
the unobserved part of the network is modeled as an Erd\"{o}s-R\'enyi random
graph, while the observable subnetwork is left arbitrary. The main result of
this work is establishing that, under this setting, local tomography is
actually possible with high probability, provided that certain conditions on
the network model are met (such as stability and symmetry of the network
combination matrix). Remarkably, such conclusion is established under the
low-observabilityregime, where the cardinality of the observable
subnetwork is fixed, while the size of the overall network scales to infinity.Comment: To appear in IEEE Transactions on Information Theor