Here's how I see it for teams that actually play one another. But I define a rival as the team you least want to lose to rather than who you most want to beat. Because a loss hurts for a long time while a win is mostly a passing emotional high.
ISU - Iowa
K-State - Ku
Ku (although they deny it) - K-State
OU - Texas
Texas - OU
oSu - OU
TxT - IDK but guessing Texas
Baylor - TCU
TCU - Baylor (perhaps Texas)
WVU (hoops dominates) - Ku
ISU - Iowa
K-State - Ku
Ku (although they deny it) - K-State
OU - Texas
Texas - OU
oSu - OU
TxT - IDK but guessing Texas
Baylor - TCU
TCU - Baylor (perhaps Texas)
WVU (hoops dominates) - Ku