%0 Journal Article %1 ISI:000308240400015 %A Roth, Camille %A Kang, Soong Moon %A Batty, Michael %A Barthelemy, Marc %C 6-9 CARLTON HOUSE TERRACE, LONDON SW1Y 5AG, ENGLAND %D 2012 %I ROYAL SOC %J JOURNAL OF THE ROYAL SOCIETY INTERFACE %K networks spatial_transportation urban_evolution %N 75 %P 2540-2550 %R 10.1098/rsif.2012.0259 %T A long-time limit for world subway networks %V 9 %X We study the temporal evolution of the structure of the world's largest subway networks in an exploratory manner. We show that, remarkably, all these networks converge to a shape that shares similar generic features despite their geographical and economic differences. This limiting shape is made of a core with branches radiating from it. For most of these networks, the average degree of a node (station) within the core has a value of order 2.5 and the proportion of k = 2 nodes in the core is larger than 60 per cent. The number of branches scales roughly as the square root of the number of stations, the current proportion of branches represents about half of the total number of stations, and the average diameter of branches is about twice the average radial extension of the core. Spatial measures such as the number of stations at a given distance to the barycentre display a first regime which grows as r(2) followed by another regime with different exponents, and eventually saturates. These results-difficult to interpret in the framework of fractal geometry-confirm and yield a natural explanation in the geometric picture of this core and their branches: the first regime corresponds to a uniform core, while the second regime is controlled by the interstation spacing on branches. The apparent convergence towards a unique network shape in the temporal limit suggests the existence of dominant, universal mechanisms governing the evolution of these structures.

@article{ISI:000308240400015, abstract = {{We study the temporal evolution of the structure of the world's largest subway networks in an exploratory manner. We show that, remarkably, all these networks converge to a shape that shares similar generic features despite their geographical and economic differences. This limiting shape is made of a core with branches radiating from it. For most of these networks, the average degree of a node (station) within the core has a value of order 2.5 and the proportion of k = 2 nodes in the core is larger than 60 per cent. The number of branches scales roughly as the square root of the number of stations, the current proportion of branches represents about half of the total number of stations, and the average diameter of branches is about twice the average radial extension of the core. Spatial measures such as the number of stations at a given distance to the barycentre display a first regime which grows as r(2) followed by another regime with different exponents, and eventually saturates. These results-difficult to interpret in the framework of fractal geometry-confirm and yield a natural explanation in the geometric picture of this core and their branches: the first regime corresponds to a uniform core, while the second regime is controlled by the interstation spacing on branches. The apparent convergence towards a unique network shape in the temporal limit suggests the existence of dominant, universal mechanisms governing the evolution of these structures.}}, added-at = {2015-05-15T21:46:32.000+0200}, address = {{6-9 CARLTON HOUSE TERRACE, LONDON SW1Y 5AG, ENGLAND}}, affiliation = {{Roth, C (Reprint Author), CAMS CNRS EHESS, 190 Ave France, F-75013 Paris, France. Roth, Camille; Barthelemy, Marc, CAMS CNRS EHESS, F-75013 Paris, France. Roth, Camille, ISC PIF, F-75005 Paris, France. Kang, Soong Moon, UCL, Dept Management Sci \& Innovat, London WC1E 6BT, England. Batty, Michael, UCL, CASA, London W1N 6TR, England. Barthelemy, Marc, CEA, IPhT, CNRS URA 2306, Inst Phys Theor, F-91191 Gif Sur Yvette, France.}}, author = {Roth, Camille and Kang, Soong Moon and Batty, Michael and Barthelemy, Marc}, author-email = {{roth@ehess.fr}}, biburl = {https://www.bibsonomy.org/bibtex/2e7426220a699c49a5106752f8512ee1f/iscpif}, cited-references = {{Angeloudis P, 2006, PHYSICA A, V367, P553, DOI 10.1016/j.physa.2005.11.007. Balcan D, 2009, P NATL ACAD SCI USA, V106, P21484, DOI 10.1073/pnas.0906910106. Barthelemy M, 2011, PHYS REP, V499, P1, DOI 10.1016/j.physrep.2010.11.002. Batty M., 2005, CITIES COMPLEXITY. BENGUIGUI L, 1991, GEOGR ANAL, V23, P362. Bettencourt LMA, 2007, P NATL ACAD SCI USA, V104, P7301, DOI 10.1073/pnas.0610172104. BON R, 1979, QUAL QUANT, V13, P307. Daganzo C. F., 2009, TRANSPORT RES B-METH, V44, P434. Derrible S, 2010, PHYSICA A, V389, P3678, DOI 10.1016/j.physa.2010.04.008. Derrible S, 2010, TRANSPORTATION, V37, P275, DOI 10.1007/s11116-009-9227-7. Gattuso D, 2005, NETW SPAT ECON, V5, P395, DOI 10.1007/s11067-005-6210-5. Haggett P, 1969, NETWORK ANAL GEOGRAP. Hanson S., 2004, GEOGRAPHY URBAN TRAN. Latora V, 2002, PHYSICA A, V314, P109, DOI 10.1016/S0378-4371(02)01089-0. Lee K, 2008, PHYSICA A, V387, P6231, DOI 10.1016/j.physa.2008.06.035. Naridi I., 1996, BAT94008 FED HIGHW A. Niedzielski MA, 2012, ANN ASSOC AM GEOGR, V102, P1409, DOI 10.1080/00045608.2011.601212. Ovenden M., 2007, TRANSIT MAPS WORLD. Reggiani A, 2009, ADV SPAT SCI, P1, DOI 10.1007/978-3-642-01554-0. Reggiani A., 2006, SPATIAL DYNAMICS NET. Seaton KA, 2004, PHYSICA A, V339, P635, DOI 10.1016/j.physa.2004.03.019. SEIDMAN SB, 1983, SOC NETWORKS, V5, P269, DOI 10.1016/0378-8733(83)90028-X. Sienkiewicz J, 2005, PHYS REV E, V72, DOI 10.1103/PhysRevE.72.046127. von Ferber C, 2009, EUR PHYS J B, V68, P261, DOI 10.1140/epjb/e2009-00090-x. Xie F, 2009, COMPUT ENVIRON URBAN, V33, P211, DOI 10.1016/j.compenvurbsys.2008.09.009. Xie F, 2007, GEOGR ANAL, V39, P336, DOI 10.1111/j.1538-4632.2007.00707.x.}}, doc-delivery-number = {{998LK}}, doi = {{10.1098/rsif.2012.0259}}, interhash = {20d261bbca079290602f4e4ef2b7109c}, intrahash = {e7426220a699c49a5106752f8512ee1f}, issn = {{1742-5689}}, journal = {{JOURNAL OF THE ROYAL SOCIETY INTERFACE}}, journal-iso = {{J. R. Soc. Interface}}, keywords = {networks spatial_transportation urban_evolution}, keywords-plus = {{METRO NETWORKS; SYSTEM}}, language = {{English}}, month = {{OCT 7}}, number = {{75}}, number-of-cited-references = {{26}}, pages = {{2540-2550}}, publisher = {{ROYAL SOC}}, research-areas = {{Science \& Technology - Other Topics}}, researcherid-numbers = {{Batty, Michael/I-5638-2014}}, times-cited = {{13}}, timestamp = {2015-06-05T00:16:42.000+0200}, title = {{A long-time limit for world subway networks}}, type = {{Article}}, unique-id = {{ISI:000308240400015}}, volume = {{9}}, web-of-science-categories = {{Multidisciplinary Sciences}}, year = 2012 }