Cost of material or information flow in complex transportation networks

Details Cost of material or information flow in complex transportation networks Cost of material or information flow in complex transportation networks

2009-08-31

arxiv.org/abs/0909.0028v1

Physics

Physics and Society

4 pages, 2 figures

Scientific paper

To analyze the transport of information or material from a source to every node of a network we use two quantities introduced in the study of river networks: the cost and the flow. For a network with $K$ nodes and $M$ levels, we show that an upper bound to the global cost is $C_{0,max}\propto KM$. From numerical simulations for spanning tree networks with scale-free topology and with $10^2$ up to $10^7$ nodes, it is found, for large $K$, that the average number of levels and the global cost are given by $M\propto \ln(K)$ and $C_0\propto K\ln (K)$, respectively. These results agree very well with the ones obtained from a mean-field approach. If the network is characterized by a degree distribution of connectivity $P(k)\propto k^{- \gamma}$, we also find that the transport efficiency increases as long as $\gamma$ decreases and that spanning tree networks with scale-free topology are more optimized to transfer information or material than random networks.

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