Popović, Marko; Štefančić, Hrvoje; Zlatić, Vinko
(2012)
Geometric origin of scaling in large traffic networks.
Physical Review Letters, 109
(20).
pp. 2087011.
ISSN 00319007
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.
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