Posted this elsewhere, but thought here also:
Playing around with a permanent rivals situation, while not perfect, a starting point. Assuming all 4 corners.
With 16 teams, you can have 3 permanent rivals and play 6 or the remaining 12 teams each year. Now to apply that to basketball, that would be a home and home with each of the 3 rivals and once against the other 12 for an 18 game conference schedule in basketball.
I generally tried to get 2 of 3 close for each of the schools and not break up any historical rivalry games. I also tried to avoid complete east west distance, ie no Utah-WVU. Also old SWC got two old SWC and old Big 8 got 2 old Big 8.
UH - Tech, BU, UCF
Tech - UH, TCU, Colorado
TCU - Tech, BU, Az St
BU - UH, TCU, BYU
Az - Az St, Utah, Ok St
Az St - AZ, TCU, BYU
Utah - BYU, Az, ISU
BYU - Utah, BU, Az St
Col - Tech, ISU, K St
Ok St - Kan, ISU, Az
Kan - Ok St, K St, Cincy
K St - Kan, Col, WVU
ISU - Col, Ok St, Utah
Cincy - WVU, UCF, Kan
WVU - Cincy, K St, UCF
UCF - UH, Cincy, WVU
If it was and 8 game conference schedule for football, just 1 permanent rival:
UH-Tech, BU-TCU
Az-Az St, BYU-Utah
Col-Ok St, Kan-K St
WVU-Cincy, ISU-UCF
Obviously not perfect, but interesting.