How much longer do you have to drive than the crow has to fly?

TL;DR

This paper investigates the relationship between road network distances and straight-line distances across various motorway networks, revealing a consistent scaling factor and proposing rules for realistic network modeling.

Contribution

It identifies a robust scaling law between network and geodetic distances and develops a model for realistic motorway network construction based on this scaling.

Findings

Typically, driving distance is 1.3 times the crow flies.

Scaling is absent in random networks, requiring non-random adjacency.

Proposed rules produce realistic motorway networks consistent with observed scaling.

Abstract

When traveling by car from one location to another, our route is constrained by the road network. The network distance between the two locations is generally longer than the geodetic distance as the crow flies. We report a systematic relation between the statistical properties of these two distances. Empirically, we find a robust scaling between network and geodetic distance distributions for a variety of large motorway networks. A simple consequence is that we typically have to drive $1.3\pm0.1$ times longer than the crow flies. This scaling is not present in standard random networks; rather, it requires non-random adjacency. We develop a set of rules to build a realistic motorway network, also consistent with the above scaling. We hypothesize that the scaling reflects a compromise between two societal needs: high efficiency and accessibility on the one hand, and limitation of costs and other burdens on the other.