Cost of material or information flow in complex transportation networks

E-ISSN： 1286-4854|90|3|30009-30009

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.90, Iss.3, 2010-06, pp. : 30009-30009

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Abstract

To analyze the transport of information or material from a source to every node of a network, in a steady-state situation, we use two quantities introduced in the study of river networks: the cost and the flow. We study a network with K+1 nodes (the source plus K nodes) and M levels. The level of a node is defined as the number of links between the source and the node. 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 10² up to 10⁷ nodes, it is found, for large K, that the average number of levels, the average level of the nodes, $\langle$ M $\rangle$, and the global cost are given by M $\propto$ ln(K), $\langle$ M $\rangle$ $\propto$ ln(K) and C₀ $\propto$ K ln(K), respectively. These asymptotic 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^-γ, we also find that the transport efficiency increases as long as γ decreases and that spanning-tree networks with scale-free topology are more optimized to transfer information or material than random networks.