  The centrality measure (CM) is one of the most fundamental metrics for
evaluating the efficiency and vulnerability analysis of complex power grids
(CPGs). Despite an abundance of different CMs for individual nodes, there are
only a few metrics available in the literature to measure the centrality of
individual lines. We propose here the current-flow (CF) line CMs to identify
the ranking of lines, where each set of lines is associated with a different
level of importance. We then find the CMs using effective resistance and apply
it to identify the important lines in a commonly used IEEE 118-bus network.
Finally, the efficiency and vulnerability of CPG are analyzed to validate the
proposed concepts.
