The angular nature of road networks

TL;DR

This paper investigates the hierarchical and geometric properties of road networks by applying a percolation process based on street segment angles, revealing phase transitions and important roads.

Contribution

It introduces a novel percolation-based method using street angles to analyze the hierarchical structure and key roads in spatially constrained networks.

Findings

Road networks exhibit a non-equilibrium first-order phase transition.

Percolation uncovers the hierarchical classification of roads.

Technique identifies the most important roads and creates a hierarchical index.

Abstract

Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore, spatially constrained, to fully understand the role that each road plays in the system it is fundamental to characterize the influence that geometrical properties have over the network's behaviour. In this work, we percolate the UK's road network using the relative angle between street segments as the occupation probability. We argue that road networks undergo a non-equilibrium first-order phase transition at the moment the main roads start to interconnect forming the spanning percolation cluster. The percolation process uncovers the hierarchical structure of the roads in the network, and as such, its classification. Furthermore, this technique serves to extract the set of most important roads of the network and to create a hierarchical index for each road in the system.