The Oracle of Notre Dame

Interesting Stats

There are 192 teams in the database.
There are 18336 possible different combinations of two teams (where the two teams need not be distinct, and could be in either order). Here is the number of combinations that yield a certain degree of separation:

Degrees of Separation Combinations

0 192

1 1904

2 6724

3 6181

4 810

5 6

Infinity 2711
After Texas A&M joined the ACC, and Pitt and Syracuse joined the ACC, there were no longer any paths with numbers greater than five.
There are 16 teams in (formerly) major conferences that have never had a change in membership. Because of this, they are only connected to the teams in their own conference. Their degree of separation from other teams is Infinity. None of these 16 teams are in FBS today.
The most separated team in the database is Chicago, whose average finite degree of separation with respect to the other teams is 3.36932.
The most connected team is Tulsa, whose average degree of separation is 1.76705.
The team that's had the most different conferencemates is Tulsa: they've been in a conference with 53 different schools.