The operation of modern power systems in such a manner that the integrity of the network will not be compromised, is a complex task. In recent times, one of the major issues, which is combating the optimal operations of modern power systems is voltage collapse. This has been a major threat to the security and the reliability of a modern power system and has been a growing concern to power system engineers, researchers and the utilities recently. A prompt identification of the sets of transmission lines whose outage could lead to a cascading failure and the sets of nodes where voltage collapse could erupt is therefore a vital issue for a reliable and secure power system operation. An alternative approach to solving these problems is therefore presented in this paper. The problem is viewed from the graph-theoretical perspective, considering the topological properties of the networks. Application of the fundamental circuit theory is employed and the Bus-to-Line matrix (BLM) is formulated. This matrix provides gives insights about the interconnections of the components of the power network. This valuable information is captured and used for identifying the critical elements where a suitable location for reactive power support could be placed to avoid voltage collapse of the network. The mathematical formulations for the traditional approach, which is power flow-based, are also presented which provides the basis for comparison purpose. An illustrative example is presented using a simple 10-bus network of the Southern Indian power system. The results obtained are compared with that obtained from the traditional power-flow based approach. The results obtained from the two approaches show a strong correlation and agreement.