  We study the effects of relaxational dynamics on congestion pressure in scale
free networks by analyzing the properties of the corresponding gradient
networks (Z. Toroczkai, K. E. Bassler, Nature {\bf 428}, 716 (2004)). Using the
Family model (F. Family, J. Phys. A, {\bf 19}, L441 (1986)) from surface-growth
physics as single-step load-balancing dynamics, we show that the congestion
pressure considerably drops on scale-free networks when compared with the same
dynamics on random graphs. This is due to a structural transition of the
corresponding gradient network clusters, which self-organize such as to reduce
the congestion pressure. This reduction is enhanced when lowering the value of
the connectivity exponent $\lambda$ towards 2.
