  We study the effects of the degree-degree correlations on the pressure
congestion J when we apply a dynamical process on scale free complex networks
using the gradient network approach. We find that the pressure congestion for
disassortative (assortative) networks is lower (bigger) than the one for
uncorrelated networks which allow us to affirm that disassortative networks
enhance transport through them. This result agree with the fact that many real
world transportation networks naturally evolve to this kind of correlation. We
explain our results showing that for the disassortative case the clusters in
the gradient network turn out to be as much elongated as possible, reducing the
pressure congestion J and observing the opposite behavior for the assortative
case. Finally we apply our model to real world networks, and the results agree
with our theoretical model.
