TY - JOUR
T1 - The outflow ranking method for weighted directed graphs
AU - van den Brink, J.R.
AU - Gilles, R.P.
PY - 2009
Y1 - 2009
N2 - 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. © 2007 Elsevier B.V. All rights reserved.
AB - 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. © 2007 Elsevier B.V. All rights reserved.
U2 - 10.1016/j.ejor.2007.11.051
DO - 10.1016/j.ejor.2007.11.051
M3 - Article
SN - 0377-2217
VL - 193
SP - 484
EP - 491
JO - European Journal of Operational Research
JF - European Journal of Operational Research
ER -
