Skip to main content

Urban road networks — spatial networks with universal geometric features?

A case study on Germany’s largest cities

Abstract

Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for the time evolution of urban road networks.

This is a preview of subscription content, access via your institution.

References

  1. S.H. Strogatz, Nature 410, 268 (2001)

    Article  ADS  Google Scholar 

  2. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)

    Article  MATH  ADS  Google Scholar 

  3. S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002)

    Article  ADS  Google Scholar 

  4. M.E.J. Newman, SIAM Rev. 45, 167 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 426, 175 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  6. D.J. Watts, Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton University Press, Princeton, 1999)

  7. Handbook of Graphs and Networks: From the Genome to the Internet, edited by S. Bornholdt, H.G. Schuster (Wiley-VCH, Weinheim, 2003)

  8. S.N. Dorogovtesev, J.F.F. Mendes, Evolution of Networks (Oxford University Press, Oxford, 2003)

  9. Statistical Mechanics of Complex Networks, edited by R. Pastor-Satorras, M. Rubi, A. Diaz-Guilera, (Springer, Berlin, 2003)

  10. Complex Networks, edited by E. Ben-Naim, H. Frauenfelder, Z. Toroczkai (Springer, Berlin, 2004)

  11. M. Marchiori, V. Latora, Physica A 285, 539 (2000)

    Article  MATH  ADS  Google Scholar 

  12. V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001)

    Article  ADS  Google Scholar 

  13. V. Latora, M. Marchiori, Physica A 314, 109 (2002)

    Article  MATH  ADS  Google Scholar 

  14. P. Sen, S. Dasgupta, A. Chatterjee, P.A. Sreeram, G. Mukherjee, S.S. Manna, Phys. Rev. E 67, 036106 (2003)

    Article  ADS  Google Scholar 

  15. K.A. Seaton, L.M. Hackett, Physica A 339, 635 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  16. I. Vragović, E. Louis, A. Díaz-Guilera, Phys. Rev. E 71, 036122 (2005)

    Article  ADS  Google Scholar 

  17. M. Kurant, P. Thiran, Phys. Rev. Lett. 96, 138701 (2006)

    Article  ADS  Google Scholar 

  18. M. Kurant, P. Thiran, Phys. Rev. E 74, 036114 (2006)

    Article  ADS  Google Scholar 

  19. K.H. Chang, K. Kim, H. Oshima, S.-M. Yoon, J. Korean Phys. Soc. 48, S143 (2006)

    Google Scholar 

  20. Z. Xu, D.Z. Sui, J. Geograph. Syst. 9, 189 (2007)

    Article  ADS  Google Scholar 

  21. W. Li, X. Cai, Physica A 382, 693 (2007)

    Article  ADS  Google Scholar 

  22. K. Lee, W.-S. Jung, J.S. Park, M.Y. Choi, Physica A 387, 6231 (2008)

    Article  ADS  Google Scholar 

  23. W. Ru, T. Jiang-Xia, W. Xin, W. Du-Juan, C. Xu, Physica A 387, 5639 (2008)

    Article  ADS  Google Scholar 

  24. A. Doménech, Physica A 388, 4658 (2009)

    Article  ADS  Google Scholar 

  25. L.A.N. Amaral, A. Scala, M. Barthélémy, H.E. Stanley, Proc. Natl. Acad. Sci. USA 97, 11149 (2000)

    Article  ADS  Google Scholar 

  26. L.-P. Chi, R. Wang, H. Su, X.-P. Xu, J.-S. Zhao, W. Li, X. Cai, Chin. Phys. Lett. 20, 1393 (2003)

    Article  ADS  Google Scholar 

  27. W. Li, X. Cai, Phys. Rev. E 69, 046106 (2004)

    Article  ADS  Google Scholar 

  28. A. Barrat, M. Barthélémy, R. Pastor-Satorras, A. Vespignani, Proc. Natl. Acad. Sci. USA 101, 3747 (2004)

    Article  ADS  Google Scholar 

  29. R. Guimerà, L.A.N. Amaral, Eur. Phys. J. B 38, 381 (2004)

    Article  ADS  Google Scholar 

  30. R. Guimerà, S. Mossa, A. Turtschi, L.A.N. Amaral, Proc. Natl. Acad. Sci. USA 102, 7794 (2005)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  31. R. Wang, X. Cai, Chin. Phys. Lett. 22, 2715 (2005)

    Article  ADS  Google Scholar 

  32. W. Li, Q.A. Wang, L. Nivanen, A. Le Méhauté, Physica A 368, 262 (2006)

  33. M. Guida, F. Maria, Chaos Solitons Fractals 31, 527 (2007)

    Article  ADS  Google Scholar 

  34. G. Bagler, Physica A 387, 2972 (2008)

    ADS  Article  Google Scholar 

  35. G. Bagler, Complex Network view of performance and rosks on Airport Networks, in Airports: Performance, Risks, and Problems, edited by P.B. Larauge, M.E. Castille (Nova, Hauppauge, 2009), pp. 199–205

  36. L.E.C. da Rocha, J. Stat. Mech. Theory Exper. P04020 (2009)

  37. J. Wu, Z. Gao, H. Sun, H. Huang, Mod. Phys. Lett. B 18, 1043 (2004)

    Article  ADS  Google Scholar 

  38. J. Sienkiewicz, J.A. Hołyst, Phys. Rev. E 72, 046127 (2005)

    Article  ADS  Google Scholar 

  39. J. Sienkiewicz, J.A. Hołyst, Acta Phys. Polon. B 36, 1771 (2005)

    ADS  Google Scholar 

  40. M.T. Gastner, M.E.J. Newman, J. Stat. Mech. Theory Exper. P01015 (2006)

  41. P. Li, X. Xiong, Z.-L. Qiao, G.-Q. Yuan, X. Sun, B.-H. Wang, Chin. Phys. Lett. 23, 3384 (2006)

    Article  ADS  Google Scholar 

  42. C. von Ferber, T. Holovatch, Yu. Holovatch, V. Palchykov, Physica A 380, 585 (2007)

    Article  ADS  Google Scholar 

  43. C. von Ferber, T. Holovatch, Yu. Holovatch, V. Palchykov, Eur. Phys. J. B 68, 261 (2009)

    Article  ADS  Google Scholar 

  44. B. Berche, C. von Ferber, T. Holovatch, Yu. Holovatch, Eur. Phys. J. B 71, 125 (2009)

    Article  ADS  Google Scholar 

  45. X. Xu, J. Hu, F. Liu, Chaos 17, 023129 (2007)

    Article  ADS  Google Scholar 

  46. Y. Hu, D. Zhu, Physica A 388, 2061 (2009)

    Article  ADS  Google Scholar 

  47. P. Kaluza, A. Kölzsch, M.T. Gastner, B. Blasius, J. R. Soc. Interface 7, 1093 (2010)

    Article  Google Scholar 

  48. M.T. Gastner, M.E.J. Newman, Eur. Phys. J. B 49, 247 (2006)

    Article  ADS  Google Scholar 

  49. P. Erdős, A. Rényi, Publ. Math. Debrecen 6, 290 (1959)

    MathSciNet  Google Scholar 

  50. B. Bollobás, Random Graphs, 2nd edn. (Cambridge University Press, Cambridge, 2001)

  51. A.-L. Barabási, R. Albert, Science 286, 509 (1999)

    Article  MathSciNet  Google Scholar 

  52. S.N. Dorogovtsev, J.F.F. Mendes, A.N. Samukhin, Phys. Rev. Lett. 85, 4633 (2000)

    Article  ADS  Google Scholar 

  53. G. Caldarelli, Scale-Free Networks – Complex Webs in Nature and Technology (Oxford University Press, Oxford, 2007)

  54. E. Schaur, Ungeplante Siedlungen/Non-planned Settlements (Krämer, Stuttgart, 1991)

  55. P. Franckhauser, La Fractalité des Structures urbaines (Anthropos, Paris, 1994)

  56. Self-Organization of Complex Structures: From Individual to Complex Dynamics, edited by F. Schweitzer (Gordon and Breach, London, 1997)

  57. W. Weidlich, G. Haag, An Integrated Model of Transport and Urban Evolution: With an Application to a Metropole of an Emerging Nation (Springer, Berlin, 1999)

  58. W. Weidlich, Sociodynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences (Harwood Academic Publishers, New York, 2000)

  59. Fundamental Principles of Urban Growth, edited by K. Humpert, K. Brenner, S. Becker (Müller and Busmann, Dortmund, 2002)

  60. F. Schweitzer, Brownian Agents and Active Particles. Collective Dynamics in the Natural and Social Sciences (Springer, Berlin, 2003)

  61. M. Batty, Cities and Complexity. Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals (MIT Press, Cambridge, 2005)

  62. C. Kühnert, D. Helbing, G.B. West, Physica A 363, 96 (2006)

    Article  ADS  Google Scholar 

  63. L.M.A. Bettencourt, J. Lobo, D. Helbing, C. Kühnert, G.B. West, Proc. Natl. Acad. Sci. USA 104, 7301 (2007)

    Article  ADS  Google Scholar 

  64. D. Helbing, C. Kühnert, S. Lämmer, A. Johansson, B. Gehlsen, H. Ammoser, G.B. West, Power laws in urban supply networks, social systems, and dense pedestrian crowds, in Complexity Perspectives in innovation and Social Change, edited by D. Lane, S. van der Leeuw, D. Pumain, G.B. West (Springer, Berlin, 2009), pp. 433–450

  65. B. Jiang, C. Claramunt, Environ. Plan. B 31, 151 (2004)

    Article  Google Scholar 

  66. B. Jiang, C. Claramunt, GeoInformatica 8, 157 (2004)

    Article  Google Scholar 

  67. S. Lämmer, B. Gehlsen, D. Helbing, Physica A 363, 89 (2006)

    Article  ADS  Google Scholar 

  68. J. Buhl, J. Gautrais, N. Reeves, R.V. Solé, S. Valverde, P. Kuntz, G. Theraulaz, Eur. Phys. J. B 49, 513 (2006)

    Article  ADS  Google Scholar 

  69. S. Scellato, A. Cardillo, V. Latora, S. Porta, Eur. Phys. J. B 50, 221 (2006)

    Article  ADS  Google Scholar 

  70. A. Cardillo, S. Scellato, V. Latora, S. Porta, Phys. Rev. E 73, 066107 (2006)

    Article  ADS  Google Scholar 

  71. P. Crucitti, V. Latora, S. Porta, Chaos 16, 015113 (2006)

    Article  ADS  Google Scholar 

  72. P. Crucitti, V. Latora, S. Porta, Phys. Rev. E 73, 036125 (2006)

    Article  ADS  Google Scholar 

  73. S. Porta, P. Crucitti, V. Latora, Environ. Plan. B 33, 705 (2006)

    Article  Google Scholar 

  74. S. Porta, P. Crucitti, V. Latora, Physica A 369, 853 (2006)

    Article  ADS  Google Scholar 

  75. V. Kalapala, V. Sanwalani, A. Clauset, C. Moore, Phys. Rev. E 73, 026130 (2006)

    Article  ADS  Google Scholar 

  76. G.B. West, Introduction to Graph Theory (Prentice Hall, Upper Saddle River, 1996)

  77. A.P. Masucci, D. Smith, A. Crooks, M. Batty, Eur. Phys. J. B 71, 259 (2009)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  78. J. Laherrère, D. Sornette, Eur. Phys. J. B 2, 525 (1998)

    Article  ADS  Google Scholar 

  79. B.M. Roehner, D. Sornette, Eur. Phys. J. B 4, 387 (1998)

    Article  ADS  Google Scholar 

  80. J.L. McCauley, G.H. Gunaratne, Physica A 329, 178 (2003)

    Article  MATH  ADS  Google Scholar 

  81. S.G. Mallat, IEEE Trans. Pat. Anal. Mach. Intell. 11, 674 (1989)

    Article  MATH  Google Scholar 

  82. B.S. Everitt, D.J. Hand, Finite Mixture Distributions (Chapmann and Hall, London, 1981)

  83. C. Godrèche, I. Kostov, I. Yekutieli, Phys. Rev. Lett. 69, 2674 (1992)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  84. M. Barthélemy, A. Flammini, Phys. Rev. Lett. 100, 138702 (2008)

    Article  ADS  Google Scholar 

  85. M. Barthélemy, A. Flammini, Netw. Spat. Econ. 9, 401 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  86. M. Batty, R. Carvalho, A. Hudson-Smith, R. Milton, D. Smith, P. Steadman, Eur. Phys. J. B 63, 303 (2008)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  87. M. Rosvall, A. Trusina, P. Minnhagen, K. Sneppen, Phys. Rev. Lett. 94, 028701 (2005)

    Article  ADS  Google Scholar 

  88. R. Wagner, Physica A 387, 2120 (2008)

    Article  ADS  Google Scholar 

  89. B. Jiang, Physica A 384, 647 (2007)

    Article  ADS  Google Scholar 

  90. J. Buhl, J. Gautrais, R.V. Solé, P. Kuntz, S. Valverde, J.L. Deneubourg, G. Theraulaz, Eur. Phys. J. B 42, 123 (2004)

    Article  ADS  Google Scholar 

  91. A. Perna, S. Valverde, J. Gautrais, C. Jost, R. Solé, P. Kuntz, G. Theraulaz, Physica A 387, 6235 (2008)

    Article  ADS  Google Scholar 

  92. T. Gross, B. Blasius, J. Roy. Soc. Interface 5, 259 (2008)

    Article  Google Scholar 

  93. Adaptive Networks – Theory, Models and Applications, edited by T. Gross, H. Sayama (Springer, Berlin, 2009)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. V. Donner.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Chan, S.H.Y., Donner, R.V. & Lämmer, S. Urban road networks — spatial networks with universal geometric features?. Eur. Phys. J. B 84, 563–577 (2011). https://doi.org/10.1140/epjb/e2011-10889-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2011-10889-3

Keywords

  • Road Network
  • Degree Distribution
  • Node Degree
  • Road Segment
  • Link Length