TL;DR
This paper provides a detailed analysis of the flow network method, which uses maximum flow concepts to rank and select teams based on competition results, ensuring desirable properties in the process.
Contribution
It offers an in-depth examination of the flow network method, highlighting its properties and applications in ranking and selection procedures.
Findings
The method constructs a complete, quasi-transitive relation on teams.
It induces ranking and selection procedures with desirable properties.
The approach is based on maximum flow concepts.
Abstract
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 (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 teams of a competition. Those procedures are proved to satisfy many desirable properties.
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