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We develop a graph theoretic approach to study topological properties of power smart networks based on the information available into the Network Topology Processor (NTP) which is a module of the Energy Management System (EMS). The NTP module continuously retains and updates electrical system topological information such as node-branch network connectivity, open-ended lines and transformers. We use this information to study two structural properties: the robustness and the connectivity. We explicitly quantify the robustness of the system and identify strongly connected subnetworks. The topological information deduced in this paper is useful for network security assessment of the system. The capabilities of the proposed approach are illustrated on one large scale network. Others topological properties could be studied based on this formulation.