We examine the fluctuation properties of packet traffic on scale-free networks and random graphs using two different dynamical rules for moving packets; random diffusion and a locally navigated diffusive motion with preferred edges. We find that preferential behaviour in either the topology or in the dynamics leads to the scaling of fluctuations of the number of packets passing nodes and the number of packets flowing along edges, respectively. We show that the absence of any preference results in the absence of scaling, and when scaling occurs it is non-universal with the scaling exponents depending on the acquisition time window, the network structure and the diffusion rule.
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