Optimal transport in weighted complex networks
Abstract
We study the patterns of optimal transport in weighted complex networks by means of the load. Packets are allowed to travel along the optimal paths, over which the total cost is minimized. The paths crucially depend on the distribution function of costs assigned to each edge. We find that in the strong disorder limit, the load distribution follows a power law both in the Erd\H{o}s-R\'enyi (ER) random graphs and in the scale-free (SF) networks, and its characteristics depends on the structure of the minimum spanning tree. Loads for a given vertex degree are highly diverse and its distribution also exhibits the SF nature similar to the whole load distribution. Finally, we measure the effect of disorder by correlation coefficients newly introduced, finding that it is larger for ER networks than for SF networks.Keywords
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