Randomized flow model and centrality measure for electrical power transmission network analysis

Commonly used centrality measures identify the most important elements in networks of components, based on the assumption that flow occurs in the network only along the shortest paths. This is not so in real networks, where different operational rules drive the flow. For this reason, a different model of flow in a network is here considered: rather than along shortest paths only, it is assumed that contributions come essentially from all paths between nodes, as simulated by random walks. Centrality measures can then be coherently defined. An example of application to an electrical power transmission system is presented.