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On the metric, topological and functional structures of urban networks

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  • Wagner, Roy

Abstract

Axial Graphs are networks whose nodes are linear axes in urban space, and whose edges represent intersections of such axes. These graphs are used in urban planning and urban morphology studies. In this paper we analyse distance distributions between nodes in axial graphs, and show that these distributions are well approximated by rescaled-Poisson distributions. We then demonstrate a correlation between the parameters governing the distance distribution and the degree of the polynomial distribution of metric lengths of linear axes in cities. This correlation provides ‘topological’ support to the metrically based categorisation of cities proposed in [R. Carvalho, A. Penn, Scaling and universality in the micro-structure of urban space, Physica A 332 (2004) 539–547]. Finally, we attempt to explain this topologico-metric categorisation in functional terms. To this end, we introduce a notion of attraction cores defined in terms of aggregations of random walk agents. We demonstrate that the number of attraction cores in cities correlates with the parameters governing their distance and line length distributions. The intersection of all the three points of view (topological, metric and agent based) yields a descriptive model of the structure of urban networks.

Suggested Citation

  • Wagner, Roy, 2008. "On the metric, topological and functional structures of urban networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2120-2132.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:8:p:2120-2132
    DOI: 10.1016/j.physa.2007.11.019
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    References listed on IDEAS

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    1. Jiang, Bin, 2007. "A topological pattern of urban street networks: Universality and peculiarity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 647-655.
    2. B Hillier & A Penn & J Hanson & T Grajewski & J Xu, 1993. "Natural Movement: Or, Configuration and Attraction in Urban Pedestrian Movement," Environment and Planning B, , vol. 20(1), pages 29-66, February.
    3. Porta, Sergio & Crucitti, Paolo & Latora, Vito, 2006. "The network analysis of urban streets: A dual approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 853-866.
    4. J. Buhl & J. Gautrais & N. Reeves & R. V. Solé & S. Valverde & P. Kuntz & G. Theraulaz, 2006. "Topological patterns in street networks of self-organized urban settlements," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(4), pages 513-522, February.
    5. Carvalho, Rui & Penn, Alan, 2004. "Scaling and universality in the micro-structure of urban space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 539-547.
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