(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)"> (This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)">
Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/hal/pseptp/hal-03153475.html
   My bibliography  Save this paper

The degree ratio ranking method for directed graphs

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)(This abstract was borrowed from another version of this item.)

Suggested Citation

  • René van den Brink & Agnieszka Rusinowska, 2021. "The degree ratio ranking method for directed graphs," PSE-Ecole d'économie de Paris (Postprint) hal-03153475, HAL.
    • Handle: RePEc:hal:pseptp:hal-03153475
    DOI: 10.1016/j.ejor.2020.06.013
    Note: View the original document on HAL open archive server: https://hal.science/hal-03153475v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03153475v1/document
    Download Restriction: no
    File URL: https://libkey.io/10.1016/j.ejor.2020.06.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. repec:hal:pseose:halshs-00941931 is not listed on IDEAS
    2. ,, 2014. "A ranking method based on handicaps," Theoretical Economics, Econometric Society, vol. 9(3), September.
    3. 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.
    4. 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.
    5. 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.
    6. Gabrielle Demange, 2012. "Collective attention and ranking methods," PSE Working Papers halshs-00564982, HAL.
    7. 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.
    8. 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.
    9. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    10. repec:hal:pseose:halshs-01109087 is not listed on IDEAS
    11. D. Bouyssou & P. Perny, 1992. "Ranking methods for valued preference relations," Post-Print hal-02920156, HAL.
    12. repec:hal:pseose:halshs-00754615 is not listed on IDEAS
    13. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    14. Denis Bouyssou & Marchant Thierry, 2018. "The β -ranking and the β -measure for directed networks: Axiomatic characterizations," Post-Print hal-02096392, HAL.
    15. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    16. 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.
    17. Denis Bouyssou & Marchant Thierry, 2018. "The β -ranking and the β -measure for directed networks: Axiomatic characterizations," Post-Print hal-02096392, HAL.
    18. 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.
    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. 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).

    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. 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. Rene van den Brink & Agnieszka Rusinowska, "undated". "The Degree Ratio Ranking Method for Directed Networks," Tinbergen Institute Discussion Papers 19-026/II, Tinbergen Institute.
    3. 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.
    4. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    5. ,, 2014. "A ranking method based on handicaps," Theoretical Economics, Econometric Society, vol. 9(3), September.
    6. Csató, László, 2019. "A characterization of the Logarithmic Least Squares Method," European Journal of Operational Research, Elsevier, vol. 276(1), pages 212-216.
    7. Bouyssou, Denis & Marchant, Thierry, 2016. "Ranking authors using fractional counting of citations: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 183-199.
    8. Germano, Fabrizio & Sobbrio, Francesco, 2020. "Opinion dynamics via search engines (and other algorithmic gatekeepers)," Journal of Public Economics, Elsevier, vol. 187(C).
    9. Daniela Bubboloni & Michele Gori, 2018. "The flow network method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 621-656, December.
    10. L'aszl'o Csat'o, 2019. "Journal ranking should depend on the level of aggregation," Papers 1904.06300, arXiv.org, revised Sep 2019.
    11. Csató, László, 2019. "Journal ranking should depend on the level of aggregation," Journal of Informetrics, Elsevier, vol. 13(4).
    12. 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.
    13. 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.
    14. P. Herings & A. Predtetchinski & A. Perea, 2006. "The Weak Sequential Core for Two-Period Economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 55-65, April.
    15. Antonin Macé, 2023. "The Limits of Citation Counts," Working Papers halshs-01630095, HAL.
    16. P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2000. "Cooperative Games in Graph Structure," Tinbergen Institute Discussion Papers 00-072/1, Tinbergen Institute.
    17. 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.
    18. G Özerol & E Karasakal, 2008. "Interactive outranking approaches for multicriteria decision-making problems with imprecise information," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1253-1268, September.
    19. Chen, Xuqi & Gao, Zhifeng & House, Lisa, 2015. "Willingness to Pay for Niche Fresh Produce across the States: Why Are Consumers Willing to Pay More for the Less Favorite?," 2015 Annual Meeting, January 31-February 3, 2015, Atlanta, Georgia 196901, Southern Agricultural Economics Association.
    20. Zhiwei Cui & Yan-An Hwang & Ding-Cheng You, 2021. "Axiomatizations of the $$\beta $$ β and the score measures in networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 399-418, June.

    More about this item

    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:hal:pseptp:hal-03153475. 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: Caroline Bauer (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.