Long-Range Connections in Transportation Networks

TL;DR

This paper demonstrates how adding a few long-range connections in three-dimensional transportation networks significantly reduces travel time and enhances robustness, illustrating the small-world effect in real-world systems.

Contribution

It introduces a spatially embedded small-world model for transportation networks and analyzes the impact of long-range links on travel efficiency and resilience.

Findings

Long-range connections reduce travel time in transportation networks.

Adding a few long-range links improves network robustness against attacks.

The small-world effect is observable in real-world spatial transportation systems.

Abstract

Since its recent introduction, the small-world effect has been identified in several important real-world systems. Frequently, it is a consequence of the existence of a few long-range connections, which dominate the original regular structure of the systems and implies each node to become accessible from other nodes after a small number of steps, typically of order $\ell \propto \log N$. However, this effect has been observed in pure-topological networks, where the nodes have no spatial coordinates. In this paper, we present an alalogue of small-world effect observed in real-world transportation networks, where the nodes are embeded in a hree-dimensional space. Using the multidimensional scaling method, we demonstrate how the addition of a few long-range connections can suubstantially reduce the travel time in transportation systems. Also, we investigated the importance of long-range connections when the systems are under an attack process. Our findings are illustrated for two real-world systems, namely the London urban network (streets and underground) and the US highways network enhanced by some of the main US airlines routes.