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A vibrational approach to node centrality and vulnerability in complex networks

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  • Estrada, Ernesto
  • Hatano, Naomichi

Abstract

We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.

Suggested Citation

  • Estrada, Ernesto & Hatano, Naomichi, 2010. "A vibrational approach to node centrality and vulnerability in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3648-3660.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:17:p:3648-3660
    DOI: 10.1016/j.physa.2010.03.030
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    Citations

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    Cited by:

    1. Ibnoulouafi, Ahmed & El Haziti, Mohamed, 2018. "Density centrality: identifying influential nodes based on area density formula," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 69-80.
    2. Paolo Bartesaghi & Michele Benzi & Gian Paolo Clemente & Rosanna Grassi & Ernesto Estrada, 2019. "Risk-dependent centrality in economic and financial networks," Papers 1907.07908, arXiv.org, revised Apr 2020.
    3. Paolo Bartesaghi & Gian Paolo Clemente & Rosanna Grassi, 2020. "Community structure in the World Trade Network based on communicability distances," Papers 2001.06356, arXiv.org, revised Jul 2020.
    4. Paolo Bartesaghi & Gian Paolo Clemente & Rosanna Grassi, 2022. "Community structure in the World Trade Network based on communicability distances," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(2), pages 405-441, April.

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