Abstract
American college football faces a conflict created by the desire to stage nationalchampionship games between the best teams of a season when there is no conventionalplay-off system for deciding which those teams are. Instead, ranking of teams is basedon their records of wins and losses during the season, but each team plays onlya small fraction of eligible opponents, making the system underdetermined orcontradictory or both. It is an interesting challenge to create a ranking systemthat at once is mathematically well founded, gives results in general accord withreceived wisdom concerning the relative strengths of the teams, and is based uponintuitive principles, allowing it to be accepted readily by fans and experts alike.Here we introduce a one-parameter ranking method that satisfies all of theserequirements and is based on a network representation of college football schedules.
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