Efficiency of Road Networks
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For any two points on the Earth, the geodesic (as the crow flies) distance between them is usually different from the travel distance (along roads). For example, the fastest driving route from Boston to Dallas is about 1750 miles long, but the geodesic distance between Boston and Dallas (as the crow flies) is only about 1520 miles. Ignoring practicality, there could have been a perfectly straight road directly from Boston to Dallas, in which case the travel distance would equal the straight line or geodesic distance. In that sense, real-world road networks are not perfectly efficient because drivers have to take routes which are not perfectly straight lines from origin to destination.
The efficiency of a route can be measured by computing the geodesic distance divided by the route length. In the case above, because the route from Boston to Dallas is about 1750 miles long and the geodesic between Boston and Dallas is about 1520 miles, the route efficiency is \(1520/1750 = 0.869\). If a route were perfectly direct, then its efficiency (by this measure) would be 1. If it were twice as long as a perfectly direct route, then its efficiency would be 0.5. In general, if a route is x times as long as the geodesic between its endpoints, then its efficiency is \(1/x\).
