The Wildcats seek their fourth victory in the last five meetings with the visiting Sun Devils when they meet for the Territorial Cup on Friday night.
Rodriguez has helped turn around a team that finished 4-8 last season, guiding Arizona (7-4, 4-4 Pac-12) to a pair of victories over Top 25 teams and a No. 24 ranking in the current BCS standings. The Wildcats have won four of their last five games after Saturday's 34-24 victory at Utah.
Rodriguez has heard plenty about the rivalry with Arizona State and finds no reason for his squad not to be prepared.
"This shouldn't be a game where I have to do all of the motivational tactics to get guys excited," Rodriguez said. "It's a rivalry game, an in-state game and a conference game. Everything is in place. This should be easy to motivate."
Graham, who was linebackers coach under Rodriguez at West Virgina, left as Pittsburgh's head coach after one season to take over the Sun Devils (6-5, 4-4), guiding them to a 5-1 start.
They had lost four straight, though, before becoming bowl eligible with Saturday's 46-7 rout of Washington State.
Graham made similar statements as Rodriguez in regards to the importance of the rivalry game.
"It is the biggest game of the year, every year," Graham said. "It is about Arizona State University winning the Territorial Cup. That's it."
To do that for the second time since 2007, Graham's team will likely need to find a way to contain Carey.
Carey ran 26 times for 204 yards and a touchdown Saturday and has an FBS-best 1,585 rushing yards while leading the nation at 144.1 per game.
The sophomore rushed for a Pac-12 record 366 yards and five touchdowns in a win over Colorado on Nov. 10, accounting for the highest single-game rushing total since Robbie Mixon of Central Michigan ran for 377 yards on Nov. 2, 2002.
"We thought coming into the season that he was one of our offensive weapons. We hoped that he would be one of the best backs in the league," Rodriguez said. "He's had a phenomenal year, and he'll keep getting better."
Graham, whose team held Washington State to one rushing yard last week after giving up 250.0 per game during its skid, knows Arizona State has a tough task ahead in trying to slow Carey.
"He is the No. 1 rusher in the country. I think he is one of the best running backs we've played," Graham said. "We have played some pretty good backs, especially in this league, but just as far as the amount of carries he has and what he does, he is as good as there is. He is, no question, the guy you have to stop and it is a tall order to do that."
Arizona State may hope to get its own running game going against an Arizona defense that ranks 11th in the Pac-12, allowing an average of 182.5 yards on the ground.
Quarterbacks Taylor Kelly and Michael Eubank combined for six touchdowns Saturday, with Kelly finishing 20 of 23 for 246 yards and four TD passes. Eubank threw for a score and ran for another.
Carey rushed 13 times for 92 yards as Arizona overcame a 10-point fourth-quarter deficit to beat Arizona State 31-27 in last season's meeting -- the third straight matchup that's been decided by four points or fewer.
Top 25 Overview
The Territorial Cup features two new head coaches (Rich Rodriguez and Todd Graham) who have their teams headed to the postseason. Arizona's Ka'Deem Carey is the nation's leading rusher, but ASU's Will Sutton is one of the top defensive linemen in the country. Besides bragging rights, there are significant recruiting implications for the state that go along with this one.