Any team that has Notre Dame on its nonconference schedule automatically receives a bump in the strength of that schedule. Even during seasons in which the Irish struggle, there at least is a bump interest for that game. Either way, any matchup with the Irish is serious business.
Jerry Palm of CBS Sports has released a piece comparing nonconference schedules for the entire Football Bowl Subdivision. For the Power Five conferences and the AAC, he lists the nonconference schedules for the teams he believes have the toughest and weakest in those conferences. Notre Dame pops up in the toughest nonconference schedule for Georgia Tech in the ACC, USC in the Pac-12, and Cincinnati in the AAC. In fact, Palm ranks the Yellow Jackets as having the fifth toughest nonconference schedule in all of the FBS.
Here are the other nonconference opponents for all the teams that have the Irish on their schedules:
Georgia Tech: Georgia, Northern Illinois, Kennesaw State
USC: BYU, San Jose State
Cincinnati: Indiana, Miami (Ohio), Murray State