Routed planar networks

Modeling a road network as a planar graph seems very natural. However, in studying continuumlimits of such networks it is useful to take routes rather than edges as primitives. This article isintended to introduce the relevant (discrete setting) notion of routed network to graph theorists. We give a naive classification of all 71 topologically different such networks on 4 leaves, and pose avariety of challenging research questions.