The central points of communication network flow has often been identifiedusing graph theoretical centrality measures. In real networks, the state oftraffic density arises from an interplay between the dynamics of the flow andthe underlying network structure. In this work we investigate the relationshipbetween centrality measures and the density of traffic for some simple particlehopping models on networks with emerging scale-free degree distributions. Wealso study how the speed of the dynamics are affected by the underlying networkstructure. Among other conclusions, we find that, even at low trafficdensities, the dynamical measure of traffic density (the occupation ratio) hasa non-trivial dependence on the static centrality (quantified by "betweennesscentrality"), which non-central vertices getting a comparatively large portionof the traffic.
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