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The degree ratio ranking method for directed graphs

Author

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  • René van den Brink

    (VU - Vrije Universiteit Amsterdam [Amsterdam])

  • Agnieszka Rusinowska

    (CNRS - Centre National de la Recherche Scientifique, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, 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)

Abstract

One of the most famous ranking methods for digraphs is the ranking by Copeland score. The Copeland score of a node in a digraph is the difference between its outdegree (i.e. its number of outgoing arcs) and its indegree (i.e. its number of ingoing arcs). In the ranking by Copeland score, a node is ranked higher, the higher is its Copeland score. In this paper, we deal with an alternative method to rank nodes according to their out- and indegree, namely ranking the nodes according to their degree ratio, i.e. the outdegree divided by the indegree. To avoid dividing by zero, we add 1 to both the out- as well as indegree of every node. We provide an axiomatization of the ranking by degree ratio using a clone property, which says that the entrance of a clone or a copy (i.e. a node that is in some sense similar to the original node) does not change the ranking among the original nodes. We also provide a new axiomatization of the ranking by Copeland score using the same axioms except that this method satisfies a different clone property. Finally, we modify the ranking by degree ratio by taking only the out- and indegree, but by definition assume nodes with indegree zero to be ranked higher than nodes with positive indegree. We provide an axiomatization of this ranking method using yet another clone property and a maximal property. In this way, we can compare the three ranking methods by their clone property.
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Suggested Citation

  • René van den Brink & Agnieszka Rusinowska, 2021. "The degree ratio ranking method for directed graphs," Post-Print hal-03153475, HAL.
  • Handle: RePEc:hal:journl:hal-03153475
    DOI: 10.1016/j.ejor.2020.06.013
    Note: View the original document on HAL open archive server: https://hal.science/hal-03153475
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    References listed on IDEAS

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    1. Gabrielle Demange, 2012. "Collective attention and ranking methods," PSE Working Papers halshs-00564982, HAL.
    2. ,, 2014. "A ranking method based on handicaps," Theoretical Economics, Econometric Society, vol. 9(3), September.
    3. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    4. Gabrielle Demange, 2012. "On the influence of a ranking system," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 431-455, July.
    5. Denis Bouyssou & Marchant Thierry, 2018. "The β -ranking and the β -measure for directed networks: Axiomatic characterizations," Post-Print hal-02096392, HAL.
    6. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    7. Du, Ye & Lehrer, Ehud & Pauzner, Ady, 2015. "Competitive economy as a ranking device over networks," Games and Economic Behavior, Elsevier, vol. 91(C), pages 1-13.
    8. de Clippel, Geoffroy & Moulin, Herve & Tideman, Nicolaus, 2008. "Impartial division of a dollar," Journal of Economic Theory, Elsevier, vol. 139(1), pages 176-191, March.
    9. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    10. Bouyssou, Denis, 1992. "Ranking methods based on valued preference relations: A characterization of the net flow method," European Journal of Operational Research, Elsevier, vol. 60(1), pages 61-67, July.
    11. van den Brink, René & Gilles, Robert P., 2009. "The outflow ranking method for weighted directed graphs," European Journal of Operational Research, Elsevier, vol. 193(2), pages 484-491, March.
    12. Giora Slutzki & Oscar Volij, 2006. "Scoring of web pages and tournaments—axiomatizations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(1), pages 75-92, January.
    13. Denis Bouyssou & Marchant Thierry, 2018. "The β -ranking and the β -measure for directed networks: Axiomatic characterizations," Post-Print hal-02096392, HAL.
    14. D. Bouyssou & P. Perny, 1992. "Ranking methods for valued preference relations," Post-Print hal-02920156, HAL.
    15. Bouyssou, D. & Perny, P., 1992. "Ranking methods for valued preference relations : A characterization of a method based on leaving and entering flows," European Journal of Operational Research, Elsevier, vol. 61(1-2), pages 186-194, August.
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    Cited by:

    1. van den Brink, René & Rusinowska, Agnieszka, 2022. "The degree measure as utility function over positions in graphs and digraphs," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1033-1044.
    2. Marzidovšek, Martin & Podpečan, Vid & Conti, Erminia & Debeljak, Marko & Mulder, Christian, 2022. "BEFANA: A tool for biodiversity-ecosystem functioning assessment by network analysis," Ecological Modelling, Elsevier, vol. 471(C).

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