Power Laws in Urban Supply Networks, Social Systems, and Dense Pedestrian Crowds

  • Dirk Helbing
  • Christian Kühnert
  • Stefan Lämmer
  • Anders Johansson
  • Björn Gehlsen
  • Hendrik Ammoser
  • Geoffrey B. West
Part of the Methodos Series book series (METH, volume 7)

The classical view of the spatio-temporal evolution of cities in developed countries is that urban spaces are the result of (centralized) urban planning. After the advent of complex systems’ theory, however, people have started to interpret city structures as a result of self-organization processes. In fact, although the dynamics of urban agglomerations is a consequence of many human decisions, these are often guided by optimization goals, requirements, constraints, or boundary conditions (such as topographic ones). Therefore, it appears promising to view urban planning decisions as results of the existing structures and upcoming ones (e.g. when a new freeway will lead close by in the near future). Within such an approach, it would not be surprising anymore if urban evolution could be understood as a result of self-organization (Batty & Longley, 1994; Frankhauser, 1994; Schweitzer, 1997).


Road Network Betweenness Centrality Hierarchical Organization Physical Review Letter Force Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adamic L. A., & Adar, E. (2003). Friends and neighbors on the web, Social Networks, 25(3), 211–230.CrossRefGoogle Scholar
  2. Albert, R., & Barabási, A. -L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97.CrossRefGoogle Scholar
  3. Baddeley, A. 1994. The magical number 7 – still magic after all these years. Psychological Review, 101(2), 353–356.CrossRefGoogle Scholar
  4. Bak, P., Christensen, K., Danon, L., & Scanlon, T. (2002). Unified scaling law for earthquakes. Physical Review Letters, 88, Article number 178501.Google Scholar
  5. Batty, M., & Longley, P. (1994). Fractal cities: A geometry of form and function. London, UK: Academic Press.Google Scholar
  6. Bettencourt, L. M. A., Lobo, J., Helbing, D., Kühnert, C., & West, G. B. (2007). Growth, innovation, scaling, and the pace of life in cities. Proceedings of the National Academy of Sciences, 104(17), 7301–7306.CrossRefGoogle Scholar
  7. Brandes, U., & Erlebach, T. (Eds.). (2005). Networks analysis. Berlin, Germany: Springer.Google Scholar
  8. Brown, J. H., & West, G. B. (2000). Scaling in biology. Oxford, UK: Oxford University Press.Google Scholar
  9. Buhl, J., Gautrais, J., Reeves, N., Solé, R. V., Valverde, S., et al. (2006). Topological patterns in street networks of self-organized urban settlements. The European Physical Journal B, 49, 513–522.CrossRefGoogle Scholar
  10. Cates, M. E., Wittmer, J. P., Bouchaud, J. P., & Claudin, P. (1998). Jamming, force chains, and fragile matter. Physical Review Letters, 81(9), 1841–1844.CrossRefGoogle Scholar
  11. } Chen, K. -Y., Fine, L. R., & Huberman, B. A. (2003). Predicting the future. Information Systems Frontiers, 5, 47–61.CrossRefGoogle Scholar
  12. Christaller, W. (1980). Die zentralen Orte in Süddeutschland (3rd ed.). Darmstadt, Germany: Wissenschaftliche Buchgesellschaft.Google Scholar
  13. Costa, L. da F., & da Rocha, L. E. C. (2006). A generalized approach to complex networks. The European Physical Journal B, 50, 237–242.Google Scholar
  14. Crucitti, P., Latora, V., & Porta, S. (2006). Centrality measures in spatial networks of urban streets. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 73(3) 036125–036129.Google Scholar
  15. Enquist, B. J., Brown, J. H., & West, G. B. (1998). Allometric scaling of plant energetics and population density. Nature 395, 163–165.CrossRefGoogle Scholar
  16. Frankhauser, P. (1994). La fractalité des structrures urbaines. Paris, France: Anthropos.Google Scholar
  17. } Fruin, J. J. (1993). The causes and prevention of crowd disasters. In R. A. Smith, & J. F. Dickie (Eds.), Engineering for crowd safety (pp 99–108). Amsterdam, The Netherlands: Elsevier.Google Scholar
  18. Gabaix, X. (1999). Zipf,s law for cities: An explanation. Quarterly Journal of Economics, 114(3), 739–767.CrossRefGoogle Scholar
  19. Gastner, M., & Newman, M. (2006). The spatial structure of networks. The European Physical Journal B, 49, 247–252.CrossRefGoogle Scholar
  20. Gautrais, J., Theraulaz, G., Deneubourg, J. -L., & Anderson, C. (2002). Emergent polyethism as a consequence of increased colony size in insect societies. Journal of Theoretical Biology, 215, 363–373.CrossRefGoogle Scholar
  21. Gibrat, R. (1931). Les Inégalités Economiques. Paris, France: Librairie du Recueil Sirey.Google Scholar
  22. Helbing, D., Ammoser, H., & Kühnert, C. (2006) Information flows in hierarchical networks and the capability of organizations to successfully respond to failures, crises, and disasters. Physica A – Statistical Mechanics and its Applications, 363(1), 141–150.CrossRefGoogle Scholar
  23. } Helbing, D., Johansson, A., Mathiesen, J., Jensen, M. H., & Hansen, A. (2006). Analytical approach to continuous and intermittent bottleneck flows. Physical Review Letters, 97, Article number 168001.Google Scholar
  24. Helbing, D., Johansson, A., & Al-Abideen, H. Z. (2007). The dynamics of crowd disasters: an empirical study. Physical Review E, 75, Article number 046109, part 2.Google Scholar
  25. HoĤyst, J. A., Sienkiewicz, J., Fronczak, A., & Suchecki, K. (2005). Scaling of distances in correlated complex networks. Physica A – Statistical Mechanics and its Applications, 351, 167–174.CrossRefGoogle Scholar
  26. Huberman, B. A., & Loch, C. H. (1996). Collaboration, motivation and the size of organizations. Journal of Organizational Computing, 6, 109–130.CrossRefGoogle Scholar
  27. Jiang, B., & Claramunt, C. (2004). A structural approach to the model generalization of an urban street network. Geoinformatica, 8(2), 157–171.CrossRefGoogle Scholar
  28. Johnson, P. A., & Jiz, X. (2005). Nonlinear dynamics, granular media and dynamic earthquake triggering. Nature, 437, 871–874.CrossRefGoogle Scholar
  29. Külbl, R., & Helbing, D. (2003). Energy laws in human travel behaviour. New Journal of Physics, 5, Article number 48.Google Scholar
  30. Kühnert, C., Helbing, D., & West, G. B. (2006). Scaling laws in urban supply networks. Physica A – Statistical Mechanics and its Applications, 363, 96–103.CrossRefGoogle Scholar
  31. Lämmer, S., Gehlsen, B., & Helbing, D. (2006). Scaling laws in the spatial structure of urban road networks. Physica A – Statistical Mechanics and its Applications, 363, 89–95.CrossRefGoogle Scholar
  32. Levinson, D., & Yerra, B. (2006). Self-organization of surface transportation networks. Transportation Science 40(2), 179–188.CrossRefGoogle Scholar
  33. Makse, H.A., Havlin, S., & Stanley, H.E. (1995). Modeling urban-growth patterns. Nature, 377, 608–612.CrossRefGoogle Scholar
  34. Miller, G. A. (1956). The magical number 7, plus or minus 2 – some limits on our capacity for processing information. The Psychological Review, 63, 81–97.CrossRefGoogle Scholar
  35. Newman, M. E. J. (2002). Assortative mixing in networks. Physical Review Letters, 89, Article number 208701.Google Scholar
  36. Porta, S., Crucitti, P., & Latora, V. (2006). The network analysis of urban streets: a primal approach. Environment and Planning B – Planning and Design, 33(5), 705–725.CrossRefGoogle Scholar
  37. Pumain, D., Paulus, F., Vacchiani, C., & Lobo, J. (2006). An evolutionary theory for interpreting urban scaling laws. Cybergeo, 343, 20p.Google Scholar
  38. Radjai, F., & Roux, S. (2002). Turbulentlike fluctuations in quasistatic flow of granular media. Physical Review Letters, 89(6), Article number 064302.Google Scholar
  39. Schweitzer, F. (Ed.). (1997). Self-organization of complex structures: From individual to collective dynamics. London, UK: Gordon and Breach.Google Scholar
  40. Schweitzer, F. (2003). Brownian agents and active particles. Berlin, Germany: Springer.Google Scholar
  41. Simon, H. (1955). On a class of skew distribution functions. Biometri ka, 42(3–4), 425–440.Google Scholar
  42. } Steindl, J. (1965). Random processes and the growth of firms. New York, NY: Hafner.Google Scholar
  43. Strumsky, D., Lobo, J., & Fleming, L. (2005). Metropolitan patenting, inventor agglomeration and social networks: a tale of two effects. Santa Fe Institute Working Paper, 05-02-004.Google Scholar
  44. Sutton, J. (1997). Gibrat’s legacy. Journal of Economics Literature, 35(1), 40–59.Google Scholar
  45. Tubbs, S. L. (2003). A systems approach to small group interaction. Boston, MA: McGraw-Hill.Google Scholar
  46. Ulschak, F. L. (1981). Small group problem solving: An aid to organizational effectiveness. Cambridge, MA: Addison-Wesley.Google Scholar
  47. West, G. B., Brown, J. H., & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276, 122–126.CrossRefGoogle Scholar
  48. Zipf, G. K. (1949). Human behaviour and the principle of least effort: An introduction to human ecology. (1st ed.). Cambridge, MA: Addison-Wesley.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Dirk Helbing
    • 1
    • 2
  • Christian Kühnert
  • Stefan Lämmer
  • Anders Johansson
  • Björn Gehlsen
  • Hendrik Ammoser
  • Geoffrey B. West
  1. 1.Institute for Transport and Economics, TU Dresden01062 DresdenGermany
  2. 2.Collegium Budapest – Institute for Advanced StudyBudapestHungary

Personalised recommendations