Shape and efficiency in growing spatial distribution networks

Abstract

We study spatial distribution networks, such as gas pipelines or train tracks, which grow from an initial source or sink of the commodity transported by the network. The efficiency depends on two properties. First, the paths to the root are ideally not much longer than the “crow flies” distance. Second, the length of all connections in the network should be low. Even though these two criteria cannot be optimized simultaneously, real networks are nevertheless nearly optimal in both respects. We propose two models to explain how this situation can arise and analyze the fractal properties of the resulting networks.