Should the BCS have waited until the Army/Navy game was played?

Following @BradEdwards_BCS on twitter, I saw him respond to, apparently, a question about the Army/Navy game and the computers.  His response was "But if a team in contention for No. 2 had beaten either Army or Navy, it could impact the computer rankings to not have that game included."

So, I went to take a look at how closely connected Alabama and Oklahoma State were to either Army or Navy.  I do this through looking at the "degrees of separation" for any two teams, e.g. 1 degree if two teams played, 2 degrees if two teams had a common opponent, etc.  What I found was interesting.

Neither Alabama or Oklahoma State played Army or Navy directly.  However, Alabama played Vanderbilt and Vanderbilt played Army.  That is a close enough connection that the Army/Navy result, especially if it were to be an upset, could change the computer's rankings.  Further, Alabama was separated from Army by 3 degrees in 9 other ways and Navy in 10 ways.  Oklahoma State was separated from Army by 3 degrees in 4 ways and Navy by 3 degrees in 4 ways.  Here is the full list:

Army-->Vanderbilt-->Alabama
Army-->Miami_OH-->Kent_St-->Alabama
Army-->Northern_Illinois-->Kent_St-->Alabama
Army-->Northwestern-->Penn_State-->Alabama
Army-->Temple-->Kent_St-->Alabama
Army-->Temple-->Penn_State-->Alabama
Army-->Vanderbilt-->Arkansas-->Alabama
Army-->Vanderbilt-->Florida-->Alabama
Army-->Vanderbilt-->Mississippi-->Alabama
Army-->Vanderbilt-->Tennessee-->Alabama

Navy-->South_Carolina-->Arkansas-->Alabama

Navy-->South_Carolina-->Auburn-->Alabama

Navy-->South_Carolina-->Florida-->Alabama

Navy-->South_Carolina-->Mississippi_St-->Alabama

Navy-->South_Carolina-->Tennessee-->Alabama

Navy-->South_Carolina-->Vanderbilt-->Alabama

Navy-->Troy-->Arkansas-->Alabama

Navy-->Troy-->North_Texas-->Alabama

Navy-->Western_Kentucky-->LSU-->Alabama

Navy-->Western_Kentucky-->North_Texas-->Alabama

Army-->Ball_St-->Oklahoma-->Oklahoma_St

Army-->Miami_OH-->Missouri-->Oklahoma_St

Army-->Northern_Illinois-->Kansas-->Oklahoma_St

Army-->Tulane-->Tulsa-->Oklahoma_St

Navy-->SMU-->Texas_A&M-->Oklahoma_St

Navy-->SMU-->Tulsa-->Oklahoma_St

Navy-->Troy-->Louisiana-Lafayette-->Oklahoma_St

Navy-->Western_Kentucky-->Louisiana-Lafayette-->Oklahoma_St

Why does this matter to a computer?  Many computer algorithms rate a team based on their opponents rating and/or strength of schedule.  Some like mine go even farther to provide for factoring in any games result in the rating of a team if the teams are connected in some way.  Obviously, the more degrees of separation, the less impact on a rating.

Some of the BCS algorithms may look at the Army-->Vanderbilt-->Alabama linkage and provide for Alabama's rating to change based on the Army/Navy game.  If Army were to lose, Vanderbilt's rating may go down, and if theirs does, might Alabama's too?  And would that be enough for Sagarin's or Wolfe's computer to move Oklahom State ahead of Alabama?  If so, then we would have only been 3 coaches votes away from Oklahoma State making the BCS championship game.  If this were to happen, it would be a pity that BCS didn't include the game.

I'll take a look at the computers after the Army/Navy game to see what happens.