Eur. Phys. J. B 68, 261-275 (2009)
https://doi.org/10.1140/epjb/e2009-00090-x

Public transport networks: empirical analysis and modeling

¹ Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK
² Physikalisches Institut, Universität Freiburg, 79104 Freiburg, Germany
³ Laboratoire de Physique des Matériaux, Université Henri Poincaré, Nancy 1, 54506 Vandœuvre les Nancy Cedex, France
⁴ Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 79011 Lviv, Ukraine
⁵ Institut für Theoretische Physik, Johannes Kepler Universität Linz, 4040 Linz, Austria

Corresponding author: ^a hol@icmp.lviv.ua

Received: 1 October 2008
Revised: 17 December 2008
Published online: 14 March 2009

Abstract

Public transport networks of fourteen cities of so far unexplored network size are analyzed in standardized graph representations: the simple graph of the network map, the bipartite graph of routes and stations, and both one mode projections of the latter. Special attention is paid to the inter-relations and spatial embedding of transport routes. This systematic approach reveals rich behavior beyond that of the ubiquitous scale-free complex network. We find strong evidence for structures in PTNs that are counter-intuitive and need to be explained, among these a pronounced diversity in the expression of typical network characteristics within the present sample of cities, a surprising geometrical behavior with respect to the two-dimensional geographical embedding and an unexpected attraction between transport routes. A simple model based on these observations reproduces many of the identified PTN properties by growing networks of attractive self-avoiding walks.