Eur. Phys. J. Special Topics 216, 49-55 (2013)
https://doi.org/10.1140/epjst/e2013-01728-0

Regular Article

Fractal transit networks: Self-avoiding walks and Lévy flights

¹ Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, UK
Heinrich-Heine Universität Düsseldorf, 40225 Düsseldorf, Germany
² Institute for Condensed Matter Physics, National Acad. Sci. of Ukraine, 79011 Lviv, Ukraine

^a e-mail: C.vonFerber@coventry.ac.uk
^b e-mail: hol@icmp.lviv.ua

Received: 30 November 2012
Revised: 6 December 2012
Published online: 31 January 2013

Abstract

Using the data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power law behaviour. This indicates that the routes may in part also be described as Lévy-flights. The latter property may result from the fact that the routes are planned to be adapted to the fluctuating demand densities throughout the served area. We also relate this to optimization properties of Lévy flights.