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We discuss a framework for quantitative vulnerability assessment of critical infrastructure systems. We focus on the smart electric power delivery systems, i.e., electricity transmission and distribution smart grids, along with SCADA and EMS systems. We introduce concepts and results from graph and social network theories, and apply them to the study of the WSCC-Smart Power Grid Network-SCADA-EMS (WSSE) System. We also calculate values of the topological characteristics of the networks and compare their error and attack tolerances, i.e., their performance when vertices are removed, randomly or in a malicious way. Also, we study the possible topology generation models such as the random graph, small-world, and scale-free models. The WSEE system was found to follow the scale-free graph model of social network theory.