The Oracle of Notre Dame

Interesting Stats

There are 185 teams in the database.
There are 17020 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

0 185

1 1606

2 4599

3 5699

4 2210

5 300

Infinity 2606
After Texas A&M joined the SEC, and Pitt and Syracuse joined the SEC, there were no longer any paths with numbers greater than five.
There are 16 teams in 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 Division I-A today.
The most separated team in the database is Chicago, whose average finite degree of separation with respect to the other teams is 3.85207.
The most connected team is Tulsa, whose average degree of separation is 1.83432. Tulsa is, not coincidentally, the team that's had the most conferencemates: 45.