We present an energy-based method to estimate centrality
in electrical networks. Here the energy between a pair of vertices denotes by
the effective resistance between them. If there is only one generation and one
load, then the centrality of an edge in our method is the difference between
the energy of network after deleting the edge and that of the original network.
Compared with the local current-flow betweenness on the IEEE 14-bus system, we
have an interesting discovery that our proposed centrality is closely related
to it in the sense of that the significance of edges under the two measures
are very similar.