The outflow ranking method for weighted directed graphs

René Van Den Brink, Robert P. Gilles

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)484-491
Number of pages8
JournalEuropean Journal of Operational Research
Issue number2
Publication statusPublished - 01 Mar 2009

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Modelling and Simulation


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