The simplicity of planar networks

Scientific Reports

Volumn 3, Issue , 2013, Pages

  Viana, Matheus P ^a   Strano, Emanuele ^b   Bordin, Patricia ^c,d   Barthelemy, Marc ^e,f  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b EPFL   (Switzerland)

^c UNIVERSITÉ PARIS EST   (France)

^d UNIVERSITÉ PARIS DESCARTES   (France)

^e DIF   (France)

^f ÉCOLE DES HAUTES ÉTUDES EN SCIENCES SOCIALES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL NEURAL NETWORK; THEORETICAL MODEL;

MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER);

EID: 84890655256     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep03495     Document Type: Article

References (33)

1. Clark, J. & Holton, D. A. A first look at graph theory (World Scientific, Teaneck, NJ, 1991).
2. Tutte, W. T. A census of planar maps. Canad. J. Math 15, 249-271 (1963).
3. Bouttier, J., Di Francesco, P. & Guitter, E. Planar maps as labeled mobiles. Electron. J. Combin 11, R69 (2004).
4. Ambjorn, J. & Jonsson, P. Quantum geometry: a statistical field theory approach (Cambridge University Press, Cambridge, UK, 1997).
5. Mileyko, Y., Edelsbrunner, H., Price, C. A. &Weitz, J. S. Hierarchical ordering of reticular networks. PLoS One 7, e36715 (2012).
6. Katifori, E. & Magnasco, M. O. Quantifying loopy network architectures. PLoS One 7, e37994 (2012).
7. Barthelemy, M. Spatial Networks. Phys. Rep. 499, 1-101 (2011).
8. Haggett, P. & Chorley, R. J. Network analysis in geography (Edward Arnold, London, 1969).
9. Xie, F. & Levinson, D. Topological evolution of surface transportation networks. Comput. Environ. Urban 33, 211-223 (2009).
10. Hillier, B. & Hanson, J. The social logic of space (Cambridge University Press, Cambridge, UK, 1984).
11. Marshall, S. Streets and Patterns (Spon Press, Abingdon, Oxon UK, 2006).
12. Southworth, M. & Ben-Joseph, E. Streets and the Shaping of Towns and Cities (Island Press, Washington DC., USA, 2003).
13. Jiang, B. & Claramunt, C. Topological analysis of urban street networks. Environ. Plann. B 31, 151-162 (2004). (Pubitemid 38225622)
14. Roswall, M., Trusina, A., Minnhagen, P. & Sneppen, K. Networks and cities: an information perspective. Phys. Rev. Lett. 94, 028701 (2005).
15. Porta, S., Crucitti, P. & Latora, V. The network analysis of urban streets: a primal approach. Environ. Plann. B 33, 705-725 (2006). (Pubitemid 44550297)
16. Porta, S., Crucitti, P. & Latora, V. The network analysis of urban streets: a dual approach. Physica A 369, 853-866 (2006).
17. Lammer, S., Gehlsen, B. & Helbing, D. Scaling laws in the spatial structure of urban road networks. Physica A 363, 89-95 (2006).
18. Crucitti, P., Latora, V. &Porta, S. Centrality measures in spatial networks of urban streets. Phy. Rev. E 73, 0361251-5 (2006).
19. Cardillo, A., Scellato, S., Latora, V. & Porta, S. Structural properties of planar graphs of urban street patterns. Phys. Rev. E 73, 066107 (2006).
20. Gastner, M. T. & Newman, M. E. J. Shape and efficiency in spatial distribution networks. JSTAT 2006.01, P01015 (2006).
21. Xie, F. & Levinson, D. Measuring the structure of road networks. Geogr. Anal. 39, 336-356 (2007). (Pubitemid 46930056)
22. Jiang, B. A topological pattern of urban street networks: universality and peculiarity. Physica A 384, 647-655 (2007). (Pubitemid 47285636)
23. Masucci, A. P., Smith, D., Crooks, A. & Batty, M. Random planar graphs and the London street network. Eur. Phys. J. B 71, 259-271 (2009).
24. Chan, S. H. Y., Donner, R. V. & Lammer, S. Urban road networks-spatial networks with universal geometric features? Eur. Phys. J. B 84, 563-577 (2011).
25. Courtat, T., Gloaguen, C. & Douady, S. Mathematics and morphogenesis of cities: A geometrical approach. Phys. Rev. E 83, 036106 (2011).
26. Strano, E., Nicosia, V., Latora, V., Porta, S. & Barthelemy, M. Elementary processes governing the evolution of road networks. Sci. Rep. 2, 296 (2012).
27. Strano, E. et al. Urban street networks: a comparative analysis of ten European cities. ArXiv.1211.0259.
28. Barthelemy, M., Bordin, P., Berestycki, H. & Gribaudi, M. Self-organization Selforganization versus top-down planning in the evolution of a city. Sci. Rep. 3, 2153 (2013).
29. Perna, A., Kuntz, P.&Douady, S. Characterization of spatial network like patterns from junction geometry. Phys. Rev. E 83, 066106 (2011).
30. Yan, G., Zhou, T., Hu, B., Fu, Z. Q. & Wang, B. H. Efficient routing on complex networks. Phys. Rev. E 73, 046108 (2006).
31. Aldous, D. J. & Shun, J. Connected Spatial Networks over Random Points and a Route-Length Statistic. Stat. Sci. 25, 275-288 (2010).
32. Dixon, P. M.,Weiner, J., Mitchell-Olds, T. &Woodley, T. Bootstrapping the Gini coefficient of inequality. Ecology 68, 1548 (1987).
33. Nakagaki, T., Kobayashi, R., Nishiura, Y. & Ueda, T. Obtaining multiple separate food sources: behavioural intelligence in the Physarum plasmodium. P. Roy. Soc. Lond. B 271, 2305-2310 (2004).