# Dresden 2006 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 10: Statistical Physics of Complex Networks I

### DY 10.5: Vortrag

### Montag, 27. März 2006, 10:45–11:00, H\"UL 186

**Metropolis Public Transport: Network Topology and Vulnerability** — •Christian von Ferber^{1,2}, Yurij Holovatch^{3,4}, Taras Holovatch^{4}, and Vasyl Palchykov^{4} — ^{1}Physikalisches Institut, Freiburg University — ^{2}Complex Systems Research, Jagellonian University, Krakow — ^{3}Institute for Condensed Matter Physics, Lviv, Ukraine — ^{4}Ivan Franko National University of Lviv, Ukraine

We analyse the public transport (PT) networks of a number of major cities of the world. While the primary network topology is defined by a set of routes each servicing an ordered series of given stations, a number of different neighborhood relations may be defined both for the routes and the stations. E.g. one either defines two stations as neighbors whenever they are serviced by a common route or only if one station is the succesor of the other in the series serviced by this route. The networks defined in this way display a number of distinguishing properties, the most striking being that often several routes proceed in parallel for a sequence of stations [1]. While other networks with real-world links like cables or neurons embedded in two or three dimensions often show similar features, these can be studied in detail in our present case. Previous studies of PT have mostly been restricted to much smaller networks and did not observe scale free behavior for which we find clear indications in the larger of the networks that we analyze. Our findings for the statistics as well as for relations between the topology and vunerability of these networks are supported by simulations of an evolutionary model of PT networks that we propose. [1] C. von Ferber, Yu. Holovatch, and V. Palchykov, Condens. Matter Phys.8:225(2005)cond-mat/0501296