Comparing spatial networks: A 'one size fits all' efficiency-driven approach

TL;DR

This paper introduces a universal methodology to evaluate and compare the efficiency of spatial network designs by estimating their upper bounds, applicable across various types of spatial networks.

Contribution

It proposes a two-step approach combining a quality function based on efficiency and an algorithm to estimate its upper bound, including a universal approximation formula.

Findings

The methodology effectively assesses spatial network quality across diverse datasets.

The universal upper bound approximation is applicable regardless of network size.

Smaller gaps between bounds and actual values indicate more optimal network designs.

Abstract

Spatial networks are a powerful framework for studying a large variety of systems belonging to a broad diversity of contexts: from transportation to biology, from epidemiology to communications, and migrations, to cite a few. Spatial networks can be described in terms of their total cost (i.e. the total amount of resources needed for building or traveling their connections). Here, we address the issue of how to gauge and compare the quality of spatial network designs (i.e. efficiency vs. total cost) by proposing a two-step methodology. Firstly, we assess the network's design by introducing a quality function based on the concept of network's efficiency. Second, we propose an algorithm to estimate computationally the upper bound of our quality function for a given network. Complementarily, we provide a universal expression to obtain an approximated upper bound to any spatial network, regardless of its size. Smaller differences between the upper bound and the empirical value correspond to better designs. Finally, we test the applicability of this analytic tool-set on spatial network data-sets of different nature.