Abstract
We study the effects of relaxational dynamics on congestion pressure in scale-free (SF) networks by analyzing the properties of the corresponding gradient networks (Toroczkai and Bassler 2004 Nature 428 716). Using the Family model (Family and Bassler 1986 J. Phys. A: Math. Gen. 19 L441) from surface-growth physics as single-step load-balancing dynamics, we show that the congestion pressure considerably drops on SF 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 so as to reduce the congestion pressure. This reduction is enhanced when lowering the value of the connectivity exponent λ towards 2.
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