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The outflow ranking method for weighted directed graphs

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  • van den Brink, René
  • Gilles, Robert P.

Abstract

A ranking method assigns to every weighted directed graph a (weak) ordering of the nodes. In this paper we axiomatize the ranking method that ranks the nodes according to their outflow using four independent axioms. Besides the well-known axioms of anonymity and positive responsiveness we introduce outflow monotonicity - meaning that in pairwise comparison between two nodes, a node is not doing worse in case its own outflow does not decrease and the other node's outflow does not increase - and order preservation - meaning that adding two weighted digraphs such that the pairwise ranking between two nodes is the same in both weighted digraphs, then this is also their pairwise ranking in the 'sum' weighted digraph. The outflow ranking method generalizes the ranking by outdegree for directed graphs, and therefore also generalizes the ranking by Copeland score for tournaments.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 193 (2009)
Issue (Month): 2 (March)
Pages: 484-491

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Handle: RePEc:eee:ejores:v:193:y:2009:i:2:p:484-491

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Web page: http://www.elsevier.com/locate/eor

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Keywords: Decision analysis Weighted directed graph Ranking method Outflow Axiomatization;

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  1. 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.
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