The chart below shows the number of 1st order (the teams play each other) and 2nd order (the teams play the same 3rd team) connections between conferences. Some conferences are paired with several 1st order connections: Big 10 and MAC, Sun Belt and SEC, WAC and MWC, for example. The number of 2nd order connections are more difficult to guess; for example, there are a large number of 2nd order connections between the ACC and MAC largely because they both play a lot of games against the Big East.
Looking at conferences with legitimate national title contenders, we quickly see where the scarcity of inter-conference connections can become a serious problem for selecting teams to play for the MNC. The ACC and Big 12 have 3 and 4, the Big 12 and Pac 12 have 1 and 3, and the SEC and Pac 12 have 2 and 2.
* A is 10 points better than B and B is 20 points better than C so A is a lot better than C, too.