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Relationships between centrality measures of networks with diameter 2

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  • Benguigui, L.
  • Porat, I.

Abstract

From an intuitive analysis of the betweeness of networks in which we detail its components (not only the basic definition of the betweeness as the number of short paths through a node), we propose a relationship between the betweeness, the degree and the clustering coefficient of a node in networks with diameter 2. We verify the validity of this relationship on seven diameter 2 networks: the global migration network, the dual networks of the underground systems of Barcelona, Tokyo, London and three model networks. We show also that the dependence of the closeness with the degree is an exact linear relation with slope equal to −1.

Suggested Citation

  • Benguigui, L. & Porat, I., 2018. "Relationships between centrality measures of networks with diameter 2," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 243-251.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:243-251
    DOI: 10.1016/j.physa.2018.03.058
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    References listed on IDEAS

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    1. Angeloudis, Panagiotis & Fisk, David, 2006. "Large subway systems as complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 553-558.
    2. Zhang, Jianhua & Xu, Xiaoming & Hong, Liu & Wang, Shuliang & Fei, Qi, 2011. "Networked analysis of the Shanghai subway network, in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4562-4570.
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    Cited by:

    1. Porat, Idan & Benguigui, Lucien, 2021. "Global migration topology analysis and modeling of directed flow network 2006–2010," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    2. Deng, ZhengHong & Xu, Jiwei & Song, Qun & Hu, Bin & Wu, Tao & Huang, Panfei, 2020. "Robustness of multi-agent formation based on natural connectivity," Applied Mathematics and Computation, Elsevier, vol. 366(C).

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