  American college football faces a conflict created by the desire to stage
national championship games between the best teams of a season when there is no
conventional playoff system to decide which those teams are. Instead, ranking
of teams is based on their record of wins and losses during the season, but
each team plays only a small fraction of eligible opponents, making the system
underdetermined or contradictory or both. It is an interesting challenge to
create a ranking system that at once is mathematically well-founded, gives
results in general accord with received wisdom concerning the relative
strengths of the teams, and is based upon intuitive principles, allowing it to
be accepted readily by fans and experts alike. Here we introduce a
one-parameter ranking method that satisfies all of these requirements and is
based on a network representation of college football schedules.
