The two may have a connection, with both cutting their basketball teeth in the Philadelphia area, but "Brotherly and Sisterly Love" was about the last thing these two showed a day before their teams squared off in Nashville, Tenn.
"We don't have a relationship," McGraw, who was born and raised in Pottstown, said of Auriemma, who immigrated with his family to Norristown from Italy when he was 7. "I think that the [civility] got lost."
OK, lots of coaches can dislike each other, especially coaches of top programs who battle year in and year out for the top rung on the ladder, but rarely do you see it openly displayed the way McGraw let loose on Auriemma at yesterday's news conference promoting the game.
"When we were in the same conference [the Big East], I think there was a modicum of [civility]," McGraw continued, "but I think after beating them and not feeling any respect from that, we lost something.
"It's a little bit like how you would feel about a bully."
Wow, that is extraordinary commentary about a fellow coach.
In my long career covering women's basketball, I've been in Auriemma's presence many times, and he unquestionably can be arrogant, condescending, obnoxious and sometimes borderline rude.
But I've never seen him act like a bully.
He is the first to acknowledge he has rubbed a lot of other coaches the wrong way, but he makes no apologies.
"I could sit here and list 10,000 coaches that don't interact with each other whose rivalries are intense," Auriemma said in response to McGraw's assertions. "This is a function of women's basketball. Sometimes, we act like girls, like we're supposed to go to dinner every night.
"We're supposed to play each other, try to beat others' brains in, try to win a national championship and compete like hell. Muffet and Geno, and then we're supposed to get together afterwards and go have a bottle of wine. That [bleep] is just not going to happen."
After years of competing in the Big East, the Irish and Huskies did not play this season, after Notre Dame defected to the Atlantic Coast Conference and UConn was relegated to the new American Athletic Conference after not being invited to stay in the "new" Big East.
Just as with the murky circumstances of why UConn and Tennessee stopped playing years ago, McGraw and Auriemma were in a "she said, he said" debate over whose fault it was.
"It's not nice for Muffet to fib during Lent," Auriemma said last month after Notre Dame implied Connecticut pulled out of the rivalry.
Auriemma might be the most disliked coach in the game among his colleagues. But, frankly, for McGraw to equate Auriemma and, by extension, his Connecticut program to bullies sounds like sour grapes.
Auriemma's running his program the right way while his team beats down just about every opponent that gets in the way is not bullying. It's succeeding at the highest level.
Like him or loathe him, Auriemma's success as a coach is to be admired, not smeared.
I doubt McGraw intended to come off like a jealous coach who hasn't gotten over the fact that UConn has been the primary roadblock that has prevented her program from reaching the highest level, but she did.
It is true that Notre Dame has beaten Connecticut in seven of their last nine meetings, but it is still the Huskies who are going for a record ninth NCAA title, while the Irish are looking for their second.
UConn beat Notre Dame in the national semifinals last season on the way to the championship.
In the 11 seasons that McGraw and Auriemma coached against each other in the Big East, UConn won nine Big East Tournaments to one for the Irish.
Both took over programs that were at rock-bottom, but in 29 seasons at Connecticut, Auriemma, who is already inducted in the Naismith Basketball Hall of Fame, has surpassed Tennessee as the elite program in women's basketball by winning 86.8 percent (878-133) of his games.
If the Huskies win, it will be Auriemma's fifth undefeated national champion.
Again McGraw, who is 751-258 in 32 seasons as a head coach, has an impressive résumé, but it falls well short of Auriemma's.
"Why is she angry? I don't know," Auriemma said of McGraw. "You have to ask her. I haven't changed in 25 years.
"How I run my program hasn't changed. The respect we have for everyone else hasn't changed. We think we are the best basketball team in the county, but we don't flaunt it."
That might change tonight if Connecticut wins the battle of unbeatens and keeps McGraw and Notre Dame from another title.