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arXiv physics/0510198physics.soc-phphysics.data-an
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道路网络的尺度不变性

Scale Invariance in Road Networks

Vamsi Kalapala, Vishal Sanwalani, Aaron Clauset, Cristopher Moore

摘要:

我们研究了美国,英国和丹麦的国家公路网的拓扑和地理结构。通过将这些网络转化为它们的对偶表示,其中道路是顶点,如果相应的道路相交,则边连接两个顶点,我们表明它们具有拓扑和地理尺度不变性。也就是说,我们证明了对于足够大的地理区域,对偶度分布遵循指数为2.2 < alpha < 2.4的幂律,并且无论旅程的长度如何,都具有基本相同的结构。为了解释这些属性,我们介绍和分析了一个简单的分形模型的道路布局,再现所观察到的结构,并建议一个可测试的连接之间的标度指数α和分形维数的道路和交叉口的位置。

英文摘要:

We study the topological and geographic structure of the national road networks of the United States, England and Denmark. By transforming these networks into their dual representation, where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect, we show that they exhibit both topological and geographic scale invariance. That is, we show that for sufficiently large geographic areas, the dual degree distribution follows a power law with exponent 2.2 < alpha < 2.4, and that journeys, regardless of their length, have a largely identical structure. To explain these properties, we introduce and analyze a simple fractal model of road placement that reproduces the observed structure, and suggests a testable connection between the scaling exponent alpha and the fractal dimensions governing the placement of roads and intersections.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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