  The topological (graph) structure of complex networks often provides valuable
information about the performance and vulnerability of the network. However,
there are multiple ways to represent a given network as a graph. Electric power
transmission and distribution networks have a topological structure that is
straightforward to represent and analyze as a graph. However, simple graph
models neglect the comprehensive connections between components that result
from Ohm's and Kirchhoff's laws. This paper describes the structure of the
three North American electric power interconnections, from the perspective of
both topological and electrical connectivity. We compare the simple topology of
these networks with that of random (Erdos and Renyi, 1959),
preferential-attachment (Barabasi and Albert, 1999) and small-world (Watts and
Strogatz, 1998) networks of equivalent sizes and find that power grids differ
substantially from these abstract models in degree distribution, clustering,
diameter and assortativity, and thus conclude that these topological forms may
be misleading as models of power systems. To study the electrical connectivity
of power systems, we propose a new method for representing electrical structure
using electrical distances rather than geographic connections. Comparisons of
these two representations of the North American power networks reveal notable
differences between the electrical and topological structure of electric power
networks.
