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Centrality measures in networks

Author

Listed:
  • 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 nationale des ponts et chaussées - 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 nationale des ponts et chaussées - 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," PSE-Ecole d'économie de Paris (Postprint) halshs-04155088, HAL.
    • Handle: RePEc:hal:pseptp:halshs-04155088
    DOI: 10.1007/s00355-023-01456-4
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    Cited by:

    1. Yang, Ruohan & Su, Kun, 2025. "Attention centrality and information efficiency," Economics Letters, Elsevier, vol. 254(C).
    2. Xu, Xiang & Yang, Wei & Li, Lingfei & Zhu, Xianqiang & Cui, Junying & Zhang, Zihan & Wu, Leilei, 2025. "TD-GCN: A novel fusion method for network topological and dynamical features," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    3. repec:hal:pseptp:halshs-04188289 is not listed on IDEAS
    4. Shen, Zhao-Li & Jiao, Yue-Hao & Wei, Yi-Kun & Wen, Chun & Carpentieri, Bruno, 2025. "Efficient hybrid PageRank centrality computation for multilayer networks," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    5. López, Susana & Molina, Elisenda & Saboyá, Martha & Tejada, Juan, 2024. "Node centrality based on its edges importance: The Position centrality," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 90-104.
    6. Lei, Xue & Xu, Xueguo, 2025. "The “spider web” of venture capital: An invisible force driving corporate green technology innovation," Technology in Society, Elsevier, vol. 82(C).
    7. Alex S. O. Toledo & Laura C. Carpi & Allbens P. F. Atman & A. P. Baêta Scarpelli, 2025. "Outlier mining in criminal networks: the role of machine learning and outlier detection models," Journal of Computational Social Science, Springer, vol. 8(2), pages 1-22, May.
    8. Shan, Yaping, 2025. "Disinformation in group chat social media network," Journal of Economic Behavior & Organization, Elsevier, vol. 231(C).
    9. Nicolas Verbeek, 2024. "‘Wolf Warriors’ in the UN Security Council? Investigating power shifts through blaming," Global Policy, London School of Economics and Political Science, vol. 15(S2), pages 38-50, May.
    10. Yang Sun & Wei Zhao & Junjie Zhou, 2025. "Influence and Connectivity in Networks: A Generating Function Approach," Papers 2508.09492, arXiv.org.
    11. Jones, Sam & Schilling, Felix & Tarp, Finn, 2026. "Politicians doing business: Evidence from Mozambique," Journal of Development Economics, Elsevier, vol. 178(C).
    12. Yang Sun & Wei Zhao & Junjie Zhou, 2024. "Sequential Network Design," Papers 2409.14136, arXiv.org, revised Nov 2025.
    13. Anna-Lena Rüland & Lise H. Andersen & Alan Kai Hassen & Carringtone Kinyanjui & Annika Ralfs & Bruno Iochins Grisci, 2025. "Science diplomacy: A global research field? Findings from a bibliometric analysis of the science diplomacy scholarship of the past twenty years," Scientometrics, Springer;Akadémiai Kiadó, vol. 130(8), pages 4697-4722, August.
    14. Ilias Aarab & Thomas Gottron, 2025. "Network topology of the Euro Area interbank market," Papers 2502.15611, arXiv.org, revised Jan 2026.
    15. Bramoullé, Yann & Genicot, Garance, 2024. "Diffusion and targeting centrality," Journal of Economic Theory, Elsevier, vol. 222(C).
    16. Stojkoski, Viktor & Lopez-Calva, Luis-Felipe & Bolch, Kimberly Blair & Fernandez,Almudena, 2024. "Development Acupuncture : The Network Structure of Multidimensional Poverty and Its Implications," Policy Research Working Paper Series 10882, The World Bank.
    17. Nizar Riane, 2025. "Rethinking Arrow--Debreu: A New Framework for Exchange, Time, and Uncertainty," Papers 2510.16003, arXiv.org, revised Nov 2025.
    18. Michela Chessa, 2025. "Politics as A (Very) Complex System: A New Methodological Approach to Studying Fragmentation within a Council," GREDEG Working Papers 2025-16, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    19. van den Brink, René & Rusinowska, Agnieszka, 2024. "Degree centrality, von Neumann–Morgenstern expected utility and externalities in networks," European Journal of Operational Research, Elsevier, vol. 319(2), pages 669-677.
    20. Della Lena, Sebastiano, 2024. "The spread of misinformation in networks with individual and social learning," European Economic Review, Elsevier, vol. 168(C).
    21. Ali N. A. Koam & Muhammad Faisal Nadeem & Ali Ahmad & Hassan A. Eshaq, 2024. "Weighted Asymmetry Index: A New Graph-Theoretic Measure for Network Analysis and Optimization," Mathematics, MDPI, vol. 12(21), pages 1-20, October.
    22. 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.
    23. Gibbs, Michael & Mengel, Friederike & Siemroth, Christoph, 2025. "Innovator Networks Within the Firm and the Quality of Innovation," IZA Discussion Papers 17966, Institute of Labor Economics (IZA).
    24. Hanbat Jeong, 2024. "Dynamic Spatial Interaction Models for a Resource Allocator's Decisions and Local Agents' Multiple Activities," Papers 2411.13810, arXiv.org, revised Jul 2025.

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