Scale Invariance in Road Networks

by Vamsi Kalapala, Vishal Sanwalani, Aaron Clauset, & Cristopher Moore arXiv.org E-print Archive, 21 Oct 2005 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 empirically show that the degree distribution of the dual is well-characterized by a power law with exponent 2.0 < alpha < 2.5, 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 connection between the scaling exponent alpha and the fractal dimensions governing the placement of roads and intersections. Read more