## Using relaxational dynamics to reduce network congestion

##### Authors
Piontti, A. L. Pastore Y
La Rocca, C. E.
Toroczkai, Z.
Braunstein, L. A.
Macri, P. A.
Lopez, E.
##### Description
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.
Comment: 10 pages, 6 figures
##### Keywords
Condensed Matter - Statistical Mechanics