IDEAS home Printed from https://ideas.repec.org/p/cvh/coecwp/2015-02.html

Measuring centrality by a generalization of degree

Author

Listed:
  • Csató, László

Abstract

Network analysis has emerged as a key technique in communication studies, economics, geography, history and sociology, among others. A fundamental issue is how to identify key nodes in a network, for which purpose a number of centrality measures have been developed. This paper proposes a new parametric family of centrality measures called generalized degree. It is based on the idea that a relationship to a more interconnected node contributes to centrality in a greater extent than a connection to a less central one. Generalized degree improves on degree by redistributing its sum over the network with the consideration of the global structure. Application of the measure is supported by a set of basic properties. A sufficient condition is given for generalized degree to be rank monotonic, excluding counter-intuitive changes in the centrality ranking after certain modifications of the network. The measure has a graph interpretation and can be calculated iteratively. Generalized degree is recommended to apply besides degree since it preserves most favorable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish between their importance.

Suggested Citation

  • Csató, László, 2015. "Measuring centrality by a generalization of degree," Corvinus Economics Working Papers (CEWP) 2015/02, Corvinus University of Budapest.
    • Handle: RePEc:cvh:coecwp:2015/02
    as

    Download full text from publisher

    File URL: https://unipub.lib.uni-corvinus.hu/1846/
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Herman Monsuur & Ton Storcken, 2004. "Centers in Connected Undirected Graphs: An Axiomatic Approach," Operations Research, INFORMS, vol. 52(1), pages 54-64, February.
    2. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    3. Lindelauf, R.H.A. & Hamers, H.J.M. & Husslage, B.G.M., 2013. "Cooperative game theoretic centrality analysis of terrorist networks: The cases of Jemaah Islamiyah and Al Qaeda," European Journal of Operational Research, Elsevier, vol. 229(1), pages 230-238.
    4. Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
    5. Julio González-Díaz & Ruud Hendrickx & Edwin Lohmann, 2014. "Paired comparisons analysis: an axiomatic approach to ranking methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 139-169, January.
    6. Andrea Landherr & Bettina Friedl & Julia Heidemann, 2010. "A Critical Review of Centrality Measures in Social Networks," Business & Information Systems Engineering: The International Journal of WIRTSCHAFTSINFORMATIK, Springer;Gesellschaft für Informatik e.V. (GI), vol. 2(6), pages 371-385, December.
    7. Chebotarev, P. Yu., 1994. "Aggregation of preferences by the generalized row sum method," Mathematical Social Sciences, Elsevier, vol. 27(3), pages 293-320, June.
    8. László Csató, 2015. "A graph interpretation of the least squares ranking method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 51-69, January.
    9. Ranjan, Gyan & Zhang, Zhi-Li, 2013. "Geometry of complex networks and topological centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3833-3845.
    10. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marijana Zekić-Sušac & Rudolf Scitovski & Goran Lešaja, 2018. "CEJOR special issue of Croatian Operational Research Society," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 531-534, September.
    2. Tibor Csendes & Csanád Imreh & József Temesi, 2017. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(4), pages 739-741, December.
    3. Ausloos, Marcel, 2024. "Hierarchy selection: New team ranking indicators for cyclist multi-stage races," European Journal of Operational Research, Elsevier, vol. 314(2), pages 807-816.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. László Csató, 2019. "An impossibility theorem for paired comparisons," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 497-514, June.
    2. Csató, László & Tóth, Csaba, 2020. "University rankings from the revealed preferences of the applicants," European Journal of Operational Research, Elsevier, vol. 286(1), pages 309-320.
    3. L'aszl'o Csat'o & Csaba T'oth, 2018. "University rankings from the revealed preferences of the applicants," Papers 1810.04087, arXiv.org, revised Feb 2020.
    4. László Csató, 2017. "On the ranking of a Swiss system chess team tournament," Annals of Operations Research, Springer, vol. 254(1), pages 17-36, July.
    5. Umed Temurshoev, 2008. "Who's Who in Networks. Wanted: the Key Group," Working Papers 08-08, NET Institute, revised Sep 2008.
    6. Yu, Senbin & Gao, Liang & Xu, Lida & Gao, Zi-You, 2019. "Identifying influential spreaders based on indirect spreading in neighborhood," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 418-425.
    7. Wang, Zhixiao & Zhao, Ya & Xi, Jingke & Du, Changjiang, 2016. "Fast ranking influential nodes in complex networks using a k-shell iteration factor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 171-181.
    8. Zhu, Xiaoyu & Hao, Rongxia, 2024. "Identifying influential nodes in social networks via improved Laplacian centrality," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    9. Mehmet Mars Seven, 2024. "Performance Rating Equilibrium," Papers 2410.19006, arXiv.org, revised Nov 2025.
    10. René van den Brink & Agnieszka Rusinowska, 2017. "The degree measure as utility function over positions in networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592181, HAL.
    11. Zhu, Xiaoyu & Hao, Rongxia, 2025. "Finding influential nodes in complex networks by integrating nodal intrinsic and extrinsic centrality," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    12. Huang, Wencheng & Li, Haoran & Yin, Yanhui & Zhang, Zhi & Xie, Anhao & Zhang, Yin & Cheng, Guo, 2024. "Node importance identification of unweighted urban rail transit network: An Adjacency Information Entropy based approach," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    13. Xu, Xiao-Ke & Wang, Xue & Xiao, Jing, 2018. "Inferring parent–child relationships by a node-remove centrality framework in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 222-232.
    14. Li, Yongli & Wu, Chong & Wang, Xiaoyu & Luo, Peng, 2014. "A network-based and multi-parameter model for finding influential authors," Journal of Informetrics, Elsevier, vol. 8(3), pages 791-799.
    15. Zenou, Yves & ,, 2014. "Local and Consistent Centrality Measures in Networks," CEPR Discussion Papers 10031, C.E.P.R. Discussion Papers.
    16. Wang Yu & Guo Jinli & Liu Han, 2017. "A New Evaluation Method of Node Importance in Directed Weighted Complex Networks," Journal of Systems Science and Information, De Gruyter, vol. 5(4), pages 367-375, August.
    17. Gómez, Daniel & Figueira, José Rui & Eusébio, Augusto, 2013. "Modeling centrality measures in social network analysis using bi-criteria network flow optimization problems," European Journal of Operational Research, Elsevier, vol. 226(2), pages 354-365.
    18. Zhang, Xiaohang & Cui, Huiyuan & Zhu, Ji & Du, Yu & Wang, Qi & Shi, Wenhua, 2017. "Measuring the dissimilarity of multiplex networks: An empirical study of international trade networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 380-394.
    19. David L. Alderson & Daniel Funk & Ralucca Gera, 2020. "Analysis of the global maritime transportation system as a layered network," Journal of Transportation Security, Springer, vol. 13(3), pages 291-325, December.
    20. Ghulam Muhiuddin & Sovan Samanta & Abdulrahman F. Aljohani & Abeer M. Alkhaibari, 2023. "A Study on Graph Centrality Measures of Different Diseases Due to DNA Sequencing," Mathematics, MDPI, vol. 11(14), pages 1-18, July.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cvh:coecwp:2015/02. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Adam Hoffmann (email available below). General contact details of provider: https://edirc.repec.org/data/bkeeehu.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.