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 300-bus 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.