Complex network theory finds its application in analysis of power grid as both share some common characteristics. By using this theory finding critical elements in power network can be achieved. As vulnerabilities of elements of the network decide the vulnerability of the total network, in this paper, vulnerability of each element is studied using two complex network models—betweenness centrality and extended betweenness. The betweenness centrality considers only topological structure of power system whereas extended betweenness is based on both topological and physical properties of the system. In the latter case, some of the electrical properties such as electrical distance, line flow limits, transmission capacities of lines and PTDF matrix are included. The standard IEEE 57 bus system has been studied based upon the above mentioned indices and following conclusions have been discussed.