The flow network method

In this paper we propose an in-depth analysis of a method, called the flow network method, which associates with any network a complete and quasi-transitive binary relation on its vertices. Such a method, originally proposed by Gvozdik (Abstracts of the VI-th Moscow conference of young scientists on cybernetics and computing. Scientific Council on Cybernetics of RAS, Moscow, p 56, 1987), is based on the concept of maximum flow. Given a competition involving two or more teams, the flow network method can be used to build a relation on the set of teams which establishes, for every ordered pair of teams, if the first one did at least as good as the second one in the competition. Such a relation naturally induces procedures for ranking teams and selecting the best k teams of a competition. Those procedures are proved to satisfy many desirable properties.