The identification of topological vulnerabilities is a prerequisite for the study of security analysis. This paper presents a graph-theoretic framework to detect the minimum set of transmission lines interconnecting subnetworks inside of a power network. Moreover, the framework is used to develop a method to classify the criticality of substations. The approach can be used with power transfer distribution factors information to gain an insight about the power system security. Sometimes the power network exhibits high vulnerability related to critical transmission lines interconnecting critical substations from a physical point of view. The quantification of structural properties can provide meaningful information needed to assess and enhance the reliability and security of power system networks. The capabilities for the topological approach are illustrated on two large-scale networks. The proposed approach provides an effective tool for both real-time and offline environments for security analysis and control.