We discuss a model for survivability of Smart Power Grid under severe emergencies and vulnerability. 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 IEEE 118 Bus system. We discuss concept of self-healing grid and intelligent adaptive islanding for IEEE 118 bus system and 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 survivability of IEEE 118 bus considering network islanding scheme under random and targeted attacks. The IEEE 118 network islanding scheme was found to be more survivable under different attacks.