This work addresses the observability properties of linear time-invariant systems that are monitored by a sensor network that provides access only to relative measurements and partial absolute observations of the state-space variables. Graph-theoretical tools are deployed to represent the information sharing links between the sensors of the network. The results are extended to multi-agent coordinated systems that are independently controlled or execute distributed control protocols. Explicit analytical conditions are derived that determine the system’s observability with respect to the spectral characteristics of the information-sharing network. The system’s observability is further investigated for multi-agent systems governed by the agreement dynamics where only a singleton measurement is available. The analysis is disseminated to the design of distributed observers where the agents have only available their relative displacement measurement from their neighbors. The distributed observer’s estimation error is rendered globally asymptotically stable by the addition of an anchor node that has access to the absolute motion of a single agent (node). The theoretical analysis is validated through numerical simulations.