—We derive a measure of “electrical centrality” for AC power networks, which describes the structure of the network as a function of its electrical topology rather than its physical topology. We compare our centrality measure to conventional measures of network structure using the IEEE 300bus network. We find that when measured electrically, power networks appear to have a scale-free network structure. Thus, unlike previous studies of the structure of power grids, we find that power networks have a number of highly-connected “hub” buses. This result, and the structure of power networks in general, is likely to have important implications for the reliability and security of power networks.