Modeling Metropolis Public Transport

We present results of a survey of public transport networks (PTNs) of selected 14 major cities of the world with PTN sizes ranging between 2000 and 46000 stations and develop an evolutionary model of these networks. The structure of these PTNs is revealed in terms of a set of neighbourhood relations both for the routes and the stations. The networks defined in this way display distinguishing properties due to the constraints of the embedding 2D geographical space and the structure of the cities. In addition to the standard characteristics of complex networks like the number of nearest neighbours, mean path length, and clustering we observe features specific to PTNs. While other networks with real-world links like cables or neurons embedded in two or three dimensions often show similar behavior, these can be studied in detail in our present case. Geographical data for the routes reveal surprising self-avoiding walk properties that we relate to the optimization of surface coverage. We propose and simulate an evolutionary growth model based on effectively interacting self-avoiding walks that reproduces the key features of PTN.

[1]  R. Solé,et al.  Optimization in Complex Networks , 2001, cond-mat/0111222.

[2]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[3]  C. von Ferber,et al.  Attack Vulnerability of Public Transport Networks , 2007, 0709.3206.

[4]  J. Hołyst,et al.  Statistical analysis of 22 public transport networks in Poland. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  K. Goh,et al.  Betweenness centrality correlation in social networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  N Mathias,et al.  Small worlds: how and why. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Massimo Marchiori,et al.  Is the Boston subway a small-world network? , 2002 .

[8]  C. von Ferber,et al.  Scaling in public transport networks , 2005 .

[9]  R. Ferrer i Cancho,et al.  Scale-free networks from optimal design , 2002, cond-mat/0204344.

[10]  Ricard V. Solé,et al.  Least effort and the origins of scaling in human language , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[11]  K. Seaton,et al.  Stations, trains and small-world networks , 2003, cond-mat/0311254.

[12]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[13]  L. Benguigui,et al.  The fractal dimension of some railway networks , 1992 .

[14]  Yurij Holovatch,et al.  Network harness: Metropolis public transport , 2007 .

[15]  Entropy-induced separation of star polymers in porous media. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Xinping Xu,et al.  Scaling and correlations in three bus-transport networks of China , 2007, 0708.2606.

[17]  A. B. Harris,et al.  Self-avoiding walks on random lattices , 1983 .

[18]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[19]  V. Latora,et al.  Harmony in the Small-World , 2000, cond-mat/0008357.

[20]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[21]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[22]  Michael T. Gastner,et al.  The spatial structure of networks , 2006 .

[23]  Arnab Chatterjee,et al.  Small-world properties of the Indian railway network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[25]  Alessandro Vespignani,et al.  Large-scale topological and dynamical properties of the Internet. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.