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Measuring centrality by a generalization of degree

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  • László Csató

    (Corvinus University of Budapest
    MTA-BCE “Lendület” Strategic Interactions Research Group)

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, 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 favourable attributes of degree, but better reflects the role of the nodes in the network and has an increased ability to distinguish among their importance.

Suggested Citation

  • László Csató, 2017. "Measuring centrality by a generalization of degree," 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 771-790, December.
    • Handle: RePEc:spr:cejnor:v:25:y:2017:i:4:d:10.1007_s10100-016-0439-6
    DOI: 10.1007/s10100-016-0439-6
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    1. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer;The Psychometric Society, vol. 31(4), pages 581-603, December.
    2. 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.
    3. Mitri Kitti, 2012. "Axioms for Centrality Scoring with Principal Eigenvectors," Discussion Papers 79, Aboa Centre for Economics.
    4. Chebotarev, P. Yu., 1994. "Aggregation of preferences by the generalized row sum method," Mathematical Social Sciences, Elsevier, vol. 27(3), pages 293-320, June.
    5. 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.
    6. Herman Monsuur & Ton Storcken, 2004. "Centers in Connected Undirected Graphs: An Axiomatic Approach," Operations Research, INFORMS, vol. 52(1), pages 54-64, February.
    7. 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.
    8. 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.
    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.
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    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.
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    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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