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The Degree Ratio Ranking Method for Directed Networks

Author

Listed:
  • Rene van den Brink

    (Vrije Universiteit Amsterdam)

  • Agnieszka Rusinowska

    (Paris School of Economics)

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 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 a zero indegree, we implicitly take the out- and indegree of the reflexive digraph. We provide an axiomatization of the ranking by degree ratio using a sybling neutrality axiom, which says that the entrance of a sybling (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 sybling neutrality. Finally, we modify the ranking by degree ratio by not considering the reflexive digraph, but by definition assume nodes with indegree zero to be ranked higher than nodes with a positive indegree. We provide an axiomatization of this ranking by modified degree ratio using yet another sybling neutrality and a maximal property. In this way, we can compare the three ranking methods by their respective sybling neutrality.

Suggested Citation

  • Rene van den Brink & Agnieszka Rusinowska, "undated". "The Degree Ratio Ranking Method for Directed Networks," Tinbergen Institute Discussion Papers 19-026/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20190026
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    References listed on IDEAS

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    1. 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.
    2. Ignacio Palacios-Huerta & Oscar Volij, 2004. "The Measurement of Intellectual Influence," Econometrica, Econometric Society, vol. 72(3), pages 963-977, May.
    3. 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.
    4. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    5. 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.
    6. 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.
    7. D. Bouyssou & P. Perny, 1992. "Ranking methods for valued preference relations," Post-Print hal-02920156, HAL.
    8. 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.
    9. repec:hal:pseose:halshs-00754615 is not listed on IDEAS
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    More about this item

    Keywords

    ranking method; degree ratio; Copeland score; directed graph; network; outdegree; indegree; axiomatization;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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