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From the betweenness centrality in street networks to structural invariants in random planar graphs

Author

Listed:
  • Alec Kirkley

    (University of Rochester)

  • Hugo Barbosa

    (University of Rochester)

  • Marc Barthelemy

    (Institut de Physique Théorique
    Centre d’Analyse et de Mathématique Sociales (CNRS/EHESS))

  • Gourab Ghoshal

    (University of Rochester
    University of Rochester)

Abstract

The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. Here we demonstrate that its statistical distribution is invariant for planar networks, that are used to model many infrastructural and biological systems. Empirical analysis of street networks from 97 cities worldwide, along with simulations of random planar graph models, indicates the observed invariance to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime corresponding to loops providing local path alternatives. Furthermore, the high betweenness nodes display a non-trivial spatial clustering with increasing spatial correlation as a function of the edge-density. Our results suggest that the spatial distribution of betweenness is a more accurate discriminator than its statistics for comparing static congestion patterns and its evolution across cities as demonstrated by analyzing 200 years of street data for Paris.

Suggested Citation

  • Alec Kirkley & Hugo Barbosa & Marc Barthelemy & Gourab Ghoshal, 2018. "From the betweenness centrality in street networks to structural invariants in random planar graphs," Nature Communications, Nature, vol. 9(1), pages 1-12, December.
    • Handle: RePEc:nat:natcom:v:9:y:2018:i:1:d:10.1038_s41467-018-04978-z
    DOI: 10.1038/s41467-018-04978-z
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    Cited by:

    1. Batac, Rene C. & Cirunay, Michelle T., 2022. "Shortest paths along urban road network peripheries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    2. Shi, Shuyang & Wang, Lin & Wang, Xiaofan, 2022. "Uncovering the spatiotemporal motif patterns in urban mobility networks by non-negative tensor decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    3. Benita, Francisco & Piliouras, Georgios, 2020. "Location, location, usage: How different notions of centrality can predict land usage in Singapore," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. Formánek, Tomáš & Sokol, Ondřej, 2022. "Location effects: Geo-spatial and socio-demographic determinants of sales dynamics in brick-and-mortar retail stores," Journal of Retailing and Consumer Services, Elsevier, vol. 66(C).
    5. Diego Altafini & Valerio Cutini, 2020. "Homothetic Behavior of Betweenness Centralities: A Multiscale Alternative Approach to Relate Cities and Large Regional Structures," Sustainability, MDPI, vol. 12(19), pages 1-20, September.
    6. Nikhil Kaza & Katherine Nesse, 2021. "Characterizing the Regional Structure in the United States: A County-based Analysis of Labor Market Centrality," International Regional Science Review, , vol. 44(5), pages 560-581, September.
    7. Yat Yen & Pengjun Zhao & Muhammad T Sohail, 2021. "The morphology and circuity of walkable, bikeable, and drivable street networks in Phnom Penh, Cambodia," Environment and Planning B, , vol. 48(1), pages 169-185, January.
    8. Laura Alessandretti & Luis Guillermo Natera Orozco & Meead Saberi & Michael Szell & Federico Battiston, 2023. "Multimodal urban mobility and multilayer transport networks," Environment and Planning B, , vol. 50(8), pages 2038-2070, October.
    9. Cirunay, Michelle T. & Batac, Rene C., 2023. "Evolution of the periphery of a self-organized road network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    10. Zexun Chen & Sean Kelty & Alexandre G. Evsukoff & Brooke Foucault Welles & James Bagrow & Ronaldo Menezes & Gourab Ghoshal, 2022. "Contrasting social and non-social sources of predictability in human mobility," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    11. Zhang, Hui & Zhan, Bo & Ouyang, Min, 2024. "Enhancing accessibility through rail transit in congested urban areas: A cross-regional analysis," Journal of Transport Geography, Elsevier, vol. 115(C).
    12. Fabio Borghetti & Cristian Giovanni Colombo & Michela Longo & Renato Mazzoncini & Leonardo Cesarini & Luigi Contestabile & Claudio Somaschini, 2021. "15-Min Station: A Case Study in North Italy City to Evaluate the Livability of an Area," Sustainability, MDPI, vol. 13(18), pages 1-18, September.
    13. Mirco Nanni & Leandro Tortosa & José F Vicent & Gevorg Yeghikyan, 2020. "Ranking places in attributed temporal urban mobility networks," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-25, October.
    14. Benita, Francisco, 2020. "Carpool to work: Determinants at the county-level in the United States," Journal of Transport Geography, Elsevier, vol. 87(C).
    15. Moreno Bonaventura & Luca Maria Aiello & Daniele Quercia & Vito Latora, 2021. "Predicting urban innovation from the US Workforce Mobility Network," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-9, December.
    16. Almeira, Nahuel & Perotti, Juan Ignacio & Chacoma, Andrés & Billoni, Orlando Vito, 2021. "Explosive dismantling of two-dimensional random lattices under betweenness centrality attacks," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    17. Lee, Minjin & Cheon, SangHyun & Son, Seung-Woo & Lee, Mi Jin & Lee, Sungmin, 2023. "Exploring the relationship between the spatial distribution of roads and universal pattern of travel-route efficiency in urban road networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    18. Zhang, Mengyao & Huang, Tao & Guo, Zhaoxia & He, Zhenggang, 2022. "Complex-network-based traffic network analysis and dynamics: A comprehensive review," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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