Geometric origin of scaling in large traffic networks

TL;DR

This paper reveals that the universal power-law exponents observed in large traffic networks originate from their geometric embedding in 2D space, providing a simple model that explains these patterns analytically and through simulations.

Contribution

The study introduces a geometric model linking traffic network exponents to the dimensionality of the embedding space, explaining their universal nature and guiding future empirical research.

Findings

Exponents relate node strength to degree as s(k)~k^{3/2}.

Link weight scales with node degrees as w_{ij}~(k_i k_j)^{1/2}.

Model predictions apply to port networks and planetary spherical geometries.

Abstract

Large scale traffic networks are an indispensable part of contemporary human mobility and international trade. Networks of airport travel or cargo ships movements are invaluable for the understanding of human mobility patterns\cite{Guimera2005}, epidemic spreading\cite{Colizza2006}, global trade\cite{Imo2006} and spread of invasive species\cite{Ruiz2000}. Universal features of such networks are necessary ingredients of their description and can point to important mechanisms of their formation. Different studies\cite{Barthelemy2010} point to the universal character of some of the exponents measured in such networks. Here we show that exponents which relate i) the strength of nodes to their degree and ii) weights of links to degrees of nodes that they connect have a geometric origin. We present a simple robust model which exhibits the observed power laws and relates exponents to the dimensionality of 2D space in which traffic networks are embedded. The model is studied both analytically and in simulations and the conditions which result with previously reported exponents are clearly explained. We show that the relation between weight strength and degree is $s(k)\sim k^{3/2}$, the relation between distance strength and degree is $s^d(k)\sim k^{3/2}$ and the relation between weight of link and degrees of linked nodes is $w_{ij}\sim(k_ik_j)^{1/2}$ on the plane 2D surface. We further analyse the influence of spherical geometry, relevant for the whole planet, on exact values of these exponents. Our model predicts that these exponents should be found in future studies of port networks and impose constraints on more refined models of port networks.