As every college football message board debater knows, winning football games is transitive. In other words, if Team A beats Team B and Team B beats Team C, the fans of Team A are perfectly within their rights to talk trash to fans of Team C. Obviously, Team A could have completely wiped the floor with Team C, they just didn't happen to play each other. If Team D happens to lose to Team C, they are also deserving of as much scorn as possible. Thus one way of ranking teams just counts how many teams' fans are permissible trash talk targets (minus those in the reverse situation).

We've reached the unfortunate time of the year when we must deal with cycles.  For instance, Tulane beat Rutgers who beat Army who beat Tulane.  In these circumstances, the transitive win goes to the team with the shortest "path".  In this case, Tulane beat Rutgers directly (path length 1) so they get the transitive win over Rutgers, even though Rutgers beat Army who beat Tulane (path length 2).  

An unfortunate by-product is that teams can be ranked below teams they beat.  However, this will only occur if a cycle exists involving the two teams. 

1 Oregon 115-0 (10-0)

Cal shut down Oregon's offense to an extent not thought possible.  In these rankings though, "You play to win the game" and that's what Oregon did.  

1 Auburn 115-0 (11-0)

All of the other transitvely-clean teams got a transitive win over Mississippi State this week, so Auburn's direct win is less helpful and they drop to a tie for first.  

3 TCU 114-0 (11-0)

Similarly, TCU's win over Utah no longer distinguishes TCU.  

3 Boise State 114-0 (9-0)

5 LSU 114-1 (9-1)

5 Stanford 114-1 (9-1)

7 Arkansas 111-8 (8-2)

With their only losses to Alabama (and Auburn, but that doesn't hurt) and the SEC's best out-of-conference win over Texas A&M, Arkansas rises to the highest position outside the top group.  

8 Alabama 109-8-2 (8-2)

9 Oklahoma State 107-10-2 (9-1)

10 Wisconsin 107-11-1 (9-1)

11 Ohio State 106-12-1 (9-1)

12 Mississippi State 103-12-4 (7-3)

Mississippi State had about as graceful a fall out of the transitively-clean group as possible.  Their "bad" loss to now #8 Alabama barely hurts at all and their wins over Kentucky, Florida and even UAB (who beat a 7-3 Southern Miss) hold up reasonably well.  

13 Nebraska 102-14-3 (9-1)

14 Oklahoma 100-15-4 (8-2)

15 Michigan State 101-17-1 (9-1)

16 Missouri 100-18-1 (8-2)

17 Texas A&M 99-20 (7-3)

18 Kansas State 97-19-3 (6-4)

19 South Carolina 93-17-9 (7-3)

20 Southern California 94-21-4 (7-3)

USCe and USCw occupy consecutive positions after their wins over Florida and Arizona.  

21 Baylor 93-22-4 (7-4)

22 Arizona 92-22-5 (7-3)

23 Iowa 90-24-5 (7-3)

24 Texas Tech 89-26-4 (5-5)

25 Florida 89-27-3 (6-4)

Top 25 conference breakdown: Big 12 8, SEC 7, Big Ten 4, Pac-10 4, MWC 1, WAC 1

26 UCLA 89-28-2 (4-5)

27 Nevada 87-27-5 (8-1)

28 Virginia Tech 87-30-2 (8-2)

29 Utah 83-28-8 (8-2)

Losing to TCU doesn't knock Utah down, but losing to a certifiably mediocre Notre Dame team will send them right out of the top 25.  

30 Texas 83-32-4 (4-6)

30 Michigan 83-32-4 (7-3)

30 California 82-31-6 (5-5)

33 Florida State 80-36-3 (7-3)

34 Iowa State 77-39-3 (5-6)

34 North Carolina 76-38-5 (6-4)

36 Tennessee 75-38-6 (4-6)

37 Air Force 76-40-3 (7-4)

38 Penn State 76-41-2 (6-4)

39 North Carolina State 72-38-9 (7-3)

40 Hawaii 72-40-7 (7-3)

41 Oregon State 72-42-5 (4-5)

42 Northwestern 73-44-2 (7-3)

42 Kentucky 70-41-8 (6-5)

44 Colorado 69-41-9 (4-6)

45 Washington 70-43-6 (3-6)

46 Miami (Fla.) 71-45-3 (7-3)

47 East Carolina 68-44-7 (6-4)

48 UCF 66-44-9 (7-3)

49 San Diego State 68-47-4 (7-3)

50 Temple 66-47-6 (8-2)

50 Navy 64-45-10 (7-3)

50 Georgia 66-47-6 (5-6)

53 Arizona State 68-50-1 (4-6)

54 Notre Dame 65-48-6 (5-5)

55 Clemson 65-49-5 (5-5)

56 Tulsa 63-52-4 (7-3)

57 Brigham Young 62-52-5 (5-5)

58 Northern Illinois 61-53-5 (8-2)

59 Southern Mississippi 60-54-5 (7-3)

60 Kansas 58-54-7 (3-7)

60 Maryland 59-55-5 (7-3)

Top 60 (of 120 FBS teams) conference analysis: Big 12 12/12, Pac-10 9/10, SEC 10/12, Big Ten 7/11, MWC 5/8, ACC 6/12, CUSA 4, WAC 3, MAC 2, Independent 2, Big East 0

62 Mississippi 59-57-3 (4-6)

62 Illinois 59-57-3 (5-5)

64 West Virginia 53-58-8 (6-3)

Ladies and gentlemen, your presumptive Big East Champion.

65 Georgia Tech 52-58-9 (5-5)

65 Fresno State 53-59-7 (6-2)

67 South Florida 51-64-4 (6-3)

68 Duke 49-65-5 (3-7)

68 Southern Methodist 48-64-7 (5-5)

70 Syracuse 47-64-8 (7-3)

71 Boston College 45-63-11 (5-5)

72 Washington State 45-67-7 (2-9)

73 Army 45-68-6 (6-4)

73 Houston 45-68-6 (5-5)

75 Connecticut 43-70-6 (5-4)

75 Virginia 43-70-6 (4-6)

77 Louisville 45-73-1 (5-5)

78 Pittsburgh 43-72-4 (5-4)

79 Purdue 41-72-6 (4-6)

80 Utah State 40-73-6 (4-6)

81 Wake Forest 40-76-3 (2-8)

82 Vanderbilt 38-75-6 (2-8)

83 Cincinnati 37-77-5 (3-6)

84 Toledo 33-75-11 (6-4)

84 Rutgers 35-77-7 (4-5)

86 Tulane 35-79-5 (4-6)

87 Minnesota 34-83-2 (2-9)

88 Indiana 31-84-4 (4-6)

After Washington State's surprise win over Oregon State, the Big Ten has the two lowest BCS teams.  

89 Marshall 29-84-6 (4-6)

89 UAB 26-81-12 (3-7)

91 Texas-El Paso 28-85-6 (6-5)

92 Miami (Ohio) 28-86-5 (6-4)

93 Florida Atlantic 27-87-5 (4-5)

94 Florida International 27-91-1 (4-5)

95 Ohio 25-91-3 (7-3)

96 Wyoming 25-92-2 (2-8)

97 Rice 23-93-3 (2-8)

97 Troy 21-91-7 (5-4)

99 Louisiana Tech 21-92-6 (4-6)

100 Louisiana-Monroe 20-94-5 (4-6)

101 Colorado State 20-95-4 (3-8)

102 Kent State 21-97-1 (4-6)

103 Idaho 20-98-1 (4-6)

104 UNLV 19-98-2 (1-8)

105 Arkansas State 16-99-4 (4-6)

106 Bowling Green 16-100-3 (2-8)

107 New Mexico 16-101-2 (1-9)

108 Buffalo 14-102-3 (2-8)

109 North Texas 12-101-6 (3-7)

110 Ball State 13-103-3 (4-7)

111 New Mexico State 11-105-3 (2-8)

112 Western Kentucky 11-106-2 (2-8)

113 Memphis 10-106-3 (1-9)

114 Middle Tennessee 8-108-3 (3-6)

114 San Jose State 9-109-1 (1-9)

116 Western Michigan 7-112 (4-6)

117 La.-Lafayette 6-113 (2-8)

118 Eastern Michigan 5-114 (1-9)

119 Central Michigan 3-115-1 (3-8)

120 Akron 0-119 (0-10)

Transitive rankings obviously aren't perfect.  One issue is that they unreasonably value long chains.  In some sense, the best information comes from the closest connection.  As an alternative, here are rankings according closest connection record.  These rankings consider only the shortest connection of the type "Team A played Team B played Team C".  If Team A beat Team B who beat Team C, then Team A gets a win over Team C.  If Team A beat Team B, but Team B lost to Team C, then the Team A vs Team B match-up is considered a no-result.  Confused?  Consider Purdue and South Carolina.  The shortest connection is Purdue-Northwestern-Vanderbilt-South Carolina.  Purdue beat Northwestern who beat Vanderbilt, but Vanderbilt lost to South Carolina.  So Purdue (and South Carolina) get a transitive tie.  

The issue with these rankings is that playing a bad team (e.g. Washington State) can hurt a fair amount, especially at the top.  Oregon cannot get wins over the non-conference teams WSU lost to, since the closest connection is through WSU and results in a tie.