Both loved and loathed for its independent status, Notre Dame is and always has been a little different. That polarizing identity has only been magnified in the era of the College Football Playoff, as the Fighting Irish are a constant X factor because of their potential to take the place of a Power 5 conference champion.

Let that sink in: With four semifinal spots, somebody from the Big Ten, SEC, ACC, Big 12 or Pac-12 will always miss out on the playoff. Add Notre Dame into the top four and down goes another one.

Irish quarterback Brandon Wimbush accounted for four touchdowns against the Trojans. Matt Cashore-USA TODAY Sports

Here we are, exactly one week before the selection committee announces its first ranking of the season, with that very real scenario still in play as one-loss Notre Dame prepares for its second straight game against a top-15 opponent in No. 14 NC State.

"We can't go home like USC and go play for the Pac-12 conference after losing their second game," Notre Dame coach Brian Kelly said on Monday, two days after beating the Trojans soundly in a win that catapulted the Irish into the playoff conversation. "We lose a second game and there's no conference championship for us. We've been preparing since January that this becomes an elimination series for us."

"This" meaning every single Saturday from here on out.

That independence Notre Dame clings to so tightly is a double-edged sword when it comes to the playoff. It allows the Irish to schedule aggressively, tailor-made to impress the committee, without having to worry about divisional bottom dwellers dragging their strength of schedule down. It also makes going undefeated -- or even finishing with just one loss -- extremely difficult.

Right now, Notre Dame's only loss is by one point to a Georgia team so good it could potentially sneak into the top four with Alabama. Notre Dame's best wins are against No. 16 Michigan State, which is still undefeated in Big Ten play but has yet to face Ohio State and Penn State, and No. 21 USC. With remaining games against NC State, undefeated No. 8 Miami and No. 20 Stanford, Notre Dame is projected to have the eighth most difficult schedule in the country, according to ESPN's Football Power Index.

That scheduling flexibility is a big reason why Kelly continues to embrace the program's independence, even at a time when the Big 12 has brought back its championship game for the sake of impressing the selection committee.

"It still puts us in a position where we have to play a challenging schedule because our 12 have to be able to stand up to somebody's 13," Kelly said. "The schedule is going to have to be challenging each and every week, but that's the great thing about the schedule, as well, is you get games like Georgia and Stanford and USC. You get these kinds of battles that go across the country that most teams don't get. They stay regional. So it's a different kind of challenge but one that we think is worthwhile for us."

Call it stubborn or brilliant, the Irish are committed to this formula, and it will determine how they fare over the long haul in this system.

"The schedule is going to have to be challenging each and every week, but that's the great thing about the schedule, as well, is you get games like Georgia and Stanford and USC. You get these kinds of battles that go across the country that most teams don't get. They stay regional. So it's a different kind of challenge but one that we think is worthwhile for us."

It's possible that Notre Dame will finish with wins over the Pac-12, Big Ten and ACC champions. NC State is the only team in the ACC's Atlantic Division that is still undefeated in league play and controls its own destiny, while Miami is still undefeated and leading the Coastal Division. Stanford or USC can still win the Pac-12. Heck, Michigan State can still win the Big Ten.

Brand name and tradition aside, how could the committee exclude any team with a résumé like that? According to FPI, the average top-25 team would only have a 7 percent chance to go 11-1 against Notre Dame's schedule. Should the Irish run the table, they would have a strength of record rating comparable to past CFP semifinalists.

So let's say they're in. Who's out?

Most likely the Pac-12 and Big 12. With Notre Dame's win over USC, the Pac-12 will need either No. 12 Washington or No. 15 Washington State to run the table to avoid having a two-loss conference champion. The Pac-12 is the only Power 5 conference without an undefeated team. According to FPI, there's a 72 percent chance the Pac-12 winner will have multiple losses and a 50 percent chance for the Big 12.

Should Notre Dame run the table and finish 11-1, though, the Irish would be the only CFP contenders the committee isn't watching on championship weekend -- the one time of the season that committee members are all watching games together. Notre Dame's regular season officially ends on Nov. 25 at Stanford. Even the Big 12 will be playing for a title on Dec. 2.

Notre Dame running back Josh Adams rushed for 191 yards and three touchdowns in a 49-14 win over USC. Joe Robbins/Getty Images

Playoff executive director Bill Hancock said the benefit of the Big 12 having its conference championship game "is not the 13th game specifically, but, rather, the opportunity for its champion to play another game against a quality opponent."

Hancock won't comment on specific teams right now, but he did say that the committee will "evaluate each team's season at face value." If teams are "clustered," he said, the committee will then apply the tiebreakers: conference championships; strength of schedule; head-to-head results; and results against common opponents.

"For an independent that doesn't have a conference championship to win," Hancock said, "the committee will consider the other factors."

The fact that the committee might even consider Notre Dame this season is a story in itself. This is a program that finished an ugly 4-8 last year, putting Kelly's job at risk and leaving the Irish out of the preseason AP top 25. Nobody was talking about quarterback Brandon Wimbush, or a veteran offensive line that has paved the way for running back Josh Adams.

That's OK, though, Kelly conceded. The Irish didn't deserve to be ranked in August.

"We needed to prove who we were as a football team again," Kelly said. "Obviously, the standard of Notre Dame football had slipped under my watch, and it was important that we make the appropriate changes to bring it back to that level that it was in '12 and '15. I don't think anybody made a mistake; I think we had to earn the respect back."

They have, for at least another week.