  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.
