  We show that in any graph, the average length of a flow path in an electrical
flow between the endpoints of a random edge is $O(\log^2 n)$. This is a
consequence of a more general result which shows that the spectral norm of the
entrywise absolute value of the transfer impedance matrix of a graph is
$O(\log^2 n)$. This result implies a simple oblivious routing scheme based on
electrical flows in the case of transitive graphs.
