复杂运输网络中的材料或信息流成本
Cost of material or information flow in complex transportation networks
摘要：
为了分析信息或物质从一个源头到网络中每个节点的运输，我们使用了在研究河流网络时引入的两个量：成本和流量。对于具有$K$节点和$M$层的网络，我们证明了全局代价的上界是$C_{0,max}\propto KM$。从数值模拟的生成树网络与无标度拓扑和$10^2$到$10^7$节点，它被发现，对于大$K$，平均层数和全局成本分别由$M\propto \ln(K)$和$C_0\propto K\ln (K)$。这些结果与用平均场方法得到的结果吻合得很好。如果网络的特点是由度分布的连接$P(k)\propto k^{- γ}$，我们还发现，传输效率增加，只要$γ$减少和无标度拓扑结构的生成树网络更优化传输信息或材料比随机网络。
英文摘要：
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 $P(k)\propto k^{- γ}$, 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.
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