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Centrality measures in networks

Author

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  • Francis Bloch

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Matthew Jackson

    (Stanford University)

  • Pietro Tebaldi

    (CUMC - Columbia University Medical Center - Columbia University [New York], NBER - National Bureau of Economic Research [New York] - NBER - The National Bureau of Economic Research)

Abstract

We show that prominent centrality measures in network analysis are all based on additively separable and linear treatments of statistics that capture a node's position in the network. This enables us to provide a taxonomy of centrality measures that distills them to varying on two dimensions: (i) which information they make use of about nodes' positions, and (ii) how that information is weighted as a function of distance from the node in question. The three sorts of information about nodes' positions that are usually used—which we refer to as "nodal statistics"—are the paths from a given node to other nodes, the walks from a given node to other nodes, and the geodesics between other nodes that include a given node. Using such statistics on nodes' positions, we also characterize the types of trees such that centrality measures all agree, and we also discuss the properties that identify some path-based centrality measures.

Suggested Citation

  • Francis Bloch & Matthew Jackson & Pietro Tebaldi, 2023. "Centrality measures in networks," Post-Print halshs-04155088, HAL.
    • Handle: RePEc:hal:journl:halshs-04155088
    DOI: 10.1007/s00355-023-01456-4
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    References listed on IDEAS

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    2. Yang Sun & Wei Zhao & Junjie Zhou, 2024. "Sequential Network Design," Papers 2409.14136, arXiv.org.
    3. Yann Bramoullé & Garance Genicot, 2024. "Diffusion and targeting centrality," Post-Print hal-04718273, HAL.
    4. René Van Den Brink & Agnieszka Rusinowska, 2023. "Degree Centrality, von Neumann-Morgenstern Expected Utility and Externalities in Networks," Documents de travail du Centre d'Economie de la Sorbonne 23012r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jun 2024.
    5. Yan Leng & Xiaowen Dong & Esteban Moro & Alex Pentland, 2024. "Long-Range Social Influence in Phone Communication Networks on Offline Adoption Decisions," Information Systems Research, INFORMS, vol. 35(1), pages 318-338, March.

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