 (independent identically distributed) the exact expression for R(l) is given by
formula_9

In the limit N →∞ and P → 0, the degree distribution becomes the power law 
formula_10
This shows in this limit, the gradient network of random network is scale-free.If the subtstrate network G is scale-free, like BA model, then the gradient network also follow the power-law with the same exponent as those of G.

The fact that topology of substrate network influence the level of congestion can be illustrated by simple example(Fig.6.