Physics – Physics and Society
Scientific paper
2005-10-21
Phys. Rev. E 73, 026130 (2006)
Physics
Physics and Society
6 pages, 10 figures; revision incorporates more rigorous statistical analyses; matches journal version
Scientific paper
10.1103/PhysRevE.73.026130
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.
Clauset Aaron
Kalapala Vamsi
Moore Cristopher
Sanwalani Vishal
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