Relationship between the detour distances and the shortest distances on a road network

It is important to clarify the impact of disasters on road networks. The purpose of this paper is to examine analytically the relationship between the detour distances and shortest distances on a road network. First, we explore numerically the relationship between the detour distances and the shortest distances by use of actual prefecture and city networks in Japan. Second, we prove that detour distances are independent of (resp. proportional to, inversely proportional to) shortest distances on a rectilinear (resp. a radial-arc, an everywhere dense) network.