大型交通网络中尺度的几何起源
Geometric origin of scaling in large traffic networks
摘要：
大规模交通网络是当代人类流动和国际贸易不可或缺的组成部分。机场旅行或货船流动的网络对于了解人类流动模式\cite{Guimera2005}、传染病传播\cite{Colizza2006}、全球贸易\cite{Imo2006}和入侵物种传播\cite{Ruiz2000}是非常宝贵的。这种网络的普遍特征是其描述的必要组成部分，可以指出其形成的重要机制。不同的研究\cite{Barthelemy2010}指出，在这样的网络中测量的一些指数的通用字符。在这里，我们表明，指数，其中涉及i）节点的强度，他们的程度和ii）的权重链接到度的节点，他们连接有一个几何起源。我们提出了一个简单的鲁棒模型，表现出所观察到的幂律和相关指数的二维空间中的交通网络嵌入的维数。该模型进行了研究，分析和模拟和条件，结果与以前报道的指数清楚地解释。证明了在平面二维曲面上，权强度与度的关系为$s(k)\sim k^{3/2}$，距离强度与度的关系为$s^d(k)\sim k^{3/2}$，链权与链节点度的关系为$w_{ij}\sim(k_ik_j)^{1/2}$.我们进一步分析了球形几何的影响，相关的整个星球上，这些指数的精确值。我们的模型预测，这些指数应该在未来的研究中发现的港口网络，并施加限制，更精细的港口网络模型。
英文摘要：
Large scale traffic networks are an indispensable part of contemporary human mobility and international trade. Networks of airport travel or cargo ships movements are invaluable for the understanding of human mobility patterns\cite{Guimera2005}, epidemic spreading\cite{Colizza2006}, global trade\cite{Imo2006} and spread of invasive species\cite{Ruiz2000}. Universal features of such networks are necessary ingredients of their description and can point to important mechanisms of their formation. Different studies\cite{Barthelemy2010} point to the universal character of some of the exponents measured in such networks. Here we show that exponents which relate i) the strength of nodes to their degree and ii) weights of links to degrees of nodes that they connect have a geometric origin. We present a simple robust model which exhibits the observed power laws and relates exponents to the dimensionality of 2D space in which traffic networks are embedded. The model is studied both analytically and in simulations and the conditions which result with previously reported exponents are clearly explained. We show that the relation between weight strength and degree is $s(k)\sim k^{3/2}$, the relation between distance strength and degree is $s^d(k)\sim k^{3/2}$ and the relation between weight of link and degrees of linked nodes is $w_{ij}\sim(k_ik_j)^{1/2}$ on the plane 2D surface. We further analyse the influence of spherical geometry, relevant for the whole planet, on exact values of these exponents. Our model predicts that these exponents should be found in future studies of port networks and impose constraints on more refined models of port networks.
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