The European Physical Journal Special Topics

, Volume 215, Issue 1, pp 135–144 | Cite as

A greedy-navigator approach to navigable city plans

  • Sang Hoon Lee
  • Petter Holme
Regular Article


We use a set of four theoretical navigability indices for street maps to investigate the shape of the resulting street networks, if they are grown by optimizing these indices. The indices compare the performance of simulated navigators (having a partial information about the surroundings, like humans in many real situations) to the performance of optimally navigating individuals. We show that our simple greedy shortcut construction strategy generates the emerging structures that are different from real road network, but not inconceivable. The resulting city plans, for all navigation indices, share common qualitative properties such as the tendency for triangular blocks to appear, while the more quantitative features, such as degree distributions and clustering, are characteristically different depending on the type of metrics and routing strategies. We show that it is the type of metrics used which determines the overall shapes characterized by structural heterogeneity, but the routing schemes contribute to more subtle details of locality, which is more emphasized in case of unrestricted connections when the edge crossing is allowed.


European Physical Journal Special Topic Degree Distribution Minimum Span Tree City Plan Connection Probability 
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  1. 1.
    S.H. Lee, P. Holme, Phys. Rev. Lett. 108, 128701 (2012)CrossRefADSGoogle Scholar
  2. 2.
    A.K. Hartmann, M. Weigt, Phase Transitions in Combinatorial Optimization Problems (Wiley-VCH, 2001)Google Scholar
  3. 3.
    T. Wolbers, M. Hegarty, Trends Cognitive Sci. 14, 138 (2010)CrossRefGoogle Scholar
  4. 4.
    R. Thomas, S. Donikian, Spatial Cognition V, LNAI 4387 (2007), p. 421Google Scholar
  5. 5.
    J.M. Kleinberg, Nature 406, 845 (2000)CrossRefADSGoogle Scholar
  6. 6.
    M. Boguñá, D. Krioukov, K.C. Claffy, Nat. Phys. 5, 74 (2008)CrossRefGoogle Scholar
  7. 7.
    M. Boguñá, D. Krioukov, Phys. Rev. Lett. 102, 058701 (2009)CrossRefADSGoogle Scholar
  8. 8.
    M. Moussaïd, D. Helbing, G. Theraulaz, Proc. Natl. Acad. Sci. USA 108, 6884 (2011)CrossRefADSGoogle Scholar
  9. 9.
    M.T. Gastner, M.E.J. Newman, Phys. Rev. E 74, 016117 (2006)CrossRefADSGoogle Scholar
  10. 10.
    G. Li, S.D.S. Reis, A.A. Moreira, S. Havlin, H.E. Stanley, J.S. Andrade, Jr. , Phys. Rev. Lett. 104, 018701 (2010)CrossRefADSGoogle Scholar
  11. 11.
    M. Brede, Phys. Rev. E 81, 025202(R) (2010)CrossRefADSGoogle Scholar
  12. 12.
    Y. Hu, Y. Wang, D. Li, S. Havlin, Z. Di, Phys. Rev. Lett. 106, 108701 (2011)CrossRefADSGoogle Scholar
  13. 13.
    W. Liu, A. Zeng, Y. Zhou,e-print [arXiv:1112.0241]Google Scholar
  14. 14.
    K.-I. Goh, G. Salvi, B. Kahng, D. Kim, Phys. Rev. Lett. 96, 018701 (2006)CrossRefADSGoogle Scholar
  15. 15.
    J.B. Kruskal, Proc. Am. Math. Soc. 7, 48 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    This rule is applied since we consider the road-like structure, where each vertex corresponds to the junctions of roads. Therefore, a new crossing point generated by a new edge can be considered as a new vertex, which effectively changes the system size, so we intentionally avoid this situationGoogle Scholar
  17. 17.
    H. Youn, M.T. Gastner, H. Jeong, Phys. Rev. Lett. 101, 128701 (2008)CrossRefADSGoogle Scholar
  18. 18.
    D.J. Watts, S.H. Strogatz, Nature 393, 409 (1998)CrossRefGoogle Scholar
  19. 19.
    Note that there are two slightly different kinds of clustering coefficients, i.e., the one averaged over the individual vertices’ clustering coefficient which is used for C(k) in this work, and the other taking the ratio of numbers of triangles to the numbers of vertex triads used for CGoogle Scholar
  20. 20.
    J. Buhl, J. Gautrais, N. Reeves, R.V. Solé, S. Valverde, P. Kuntz, G. Theraulaz, Eur. Phys. J. B 49, 513 (2006)CrossRefADSGoogle Scholar
  21. 21.
    E. Strano, V. Nicosia, V. Latora, S. Porta, M. Barthélemy, Sci. Rep. 2, 296 (2012)CrossRefADSGoogle Scholar
  22. 22.
    G. Bianconi, A.-L. Barabási, Phys. Rev. Lett. 86, 5632 (2001)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.IceLab, Department of Physics, Umeå UniversityUmeåSweden
  2. 2.Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of OxfordOxfordUK
  3. 3.Department of Energy ScienceSungkyunkwan UniversitySuwonKorea
  4. 4.Department of SociologyStockholm UniversityStockholmSweden

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