It's how they have won that adds to the significance of the potential rivalry.
There was the 48-0 pounding the Cavaliers gave Miami in 2007 in the Hurricanes' last appearance in the longtime home at the Orange Bowl stadium, an embarrassing bow out that also kept the Hurricanes out of the postseason with a 5-7 record.
And last year the Cavaliers knocked Miami quarterback Jacory Harris out of the game with a hard (and legal) hit in the first quarter and went on to a 24-19 win that, in retrospect, could have been the beginning of the end for Randy Shannon's coaching stint.
Al Golden is at the helm now, however, and he said revenge will not be a factor in the Thursday night game.
"I'm not a revenge guy," said Golden, who has his Hurricanes above .500 at 4-3 after the last two wins (2-2 in the ACC). "I don't believe in it. I'm a process guy.
"The only thing that endures is the process. Everything else makes you go high and low, develops these oscillations in your program. I don't believe it. I really don't."
That's for him. Does that message get through to the players?
"I hope," Golden said, repeating himself. "I hope. I hope. I'm trying to make sure they understand that. We're making progress."
The game against the Cavaliers is the middle one in a stretch of three consecutive home outings. The Hurricanes beat Georgia Tech in the first of the three. The last is on Nov. 5 when Duke visits.
--Miami coach Al Golden saw his old boss at Virginia on the opposite sideline when Georgia Tech visited. Golden was on the staff at Virginia when Al Groh, now Tech's defensive coordinator, was head coach there. Now Golden will be facing an old colleague from Groh's staff in current Cavaliers' coach Mike London.
"Mike London is a good friend and a tremendous coach and person," Golden said.
--Miami has made significant strides in three areas of emphasis in coach Al Golden's first season. The Hurricanes are No. 50 in turnover margin in FBS statistics, up from No. 104; No. 43 in fewest penalties per game, up from No. 117; and No. 16 in fewest penalty yards per game, up from No. 113.
--Miami has been penalized only four times for 24 yards in the last two games, both wins (North Carolina and Georgia Tech). In the loss to Virginia Tech that preceded those two games, the Hurricanes were penalized nine times for 84 yards, prompting Golden to criticize some of his players for what he called "selfish" penalties.
SERIES HISTORY: Miami leads Virginia 5-3 (last meeting, 2010, Virginia 24-19).
SCOUTING THE OFFENSE: Miami didn't get a lot of yards in its win over Georgia Tech (only 262 in total offense) but got what it needed for the 24-7 win. The Hurricanes are running the ball behind sophomore RB Lamar Miller, junior Mike James, and, more recently, sophomore Eduardo Clements for about 154 yards a game. QB Jacory Harris is passing for 207 yards a game and, more importantly, has thrown only one interception in his last four outings.
SCOUTING THE DEFENSE: Miami's defense has been a work in progress, and that progress showed up when the Hurricanes held Georgia Tech to a season-low 134 yards rushing. The Hurricanes were without five starters on the defense when the season began, and though they have lost DT Marcus Forston to injury, they have all those players back now that DE Olivier Vernon is off a six-game suspension. He is being worked into the rotation in a backup role.
QUOTE TO NOTE: "No. Coach Groh kept us too busy, I'll promise you that." -- Coach Al Golden, asked if he and colleague Mike London ever discussed the possibility of becoming head coaches when they were together on Al Groh's staff at Virginia (2001-04).
STRATEGY AND PERSONNEL
THIS WEEK'S GAME: Virginia at Miami, Oct. 27 -- The Cavaliers are coming off a surprising loss to North Carolina State in their last outing and are 4-3 on the season. The wins include a three-point decision over Georgia Tech on Oct. 15.
KEYS TO THE GAME: Play an efficient game. The Hurricanes need to control the clock with their ground game and not make critical turnovers, especially at their end of the field. Virginia's defense is holding opponents to just over 138 rushing yards a game.
PLAYERS TO WATCH:
RB Lamar Miller -- After rushing for better than 100 yards in each of his first five games, the sophomore has been held to 122 total yards in the last two games combined. But he still is a threat to break off a big run at any moment.
WR Tommy Streeter -- The junior has moved up to the first unit on the depth chart after steady play in the early going. At 6-5, he is a big target and has good speed. He ranks second on the team in receptions (21) and leads in receiving yards (428) and touchdowns receptions (5).
LB Sean Spence -- Spence will be back at his usual outside spot after starting in the middle against Georgia Tech, where he could take advantage of his quickness to get to both sides of the field in defending Tech's option attack. He leads the team in tackles (65) despite missing the opener while serving a one-game suspension.
--Redshirt freshman RT Jon Feliciano, injured during a post-touchdown celebration against Georgia Tech, likely will miss the game against Virginia.
--Redshirt freshman RT Malcolm Bunche beat out sophomore Seantrel Henderson for a starting spot.
--Junior DT Darius Smith retained his No. 1 spot on the depth chart over senior DT Micanor Regis, who was suspended for the Tech game because of his actions the previous week against North Carolina.
--Sophomore DE Shayon Green remains out with a knee injury.