Graham played in every game his freshman season, posting averages of 5.9 points and 2.7 rebounds in 14 minutes per game.
His sophomore season was supposed to be a breakout year, but a partially torn patella tendon limited his game, though he still managed to up his numbers in each statistical category.
He never complained or allowed the pain to become an excuse. He was a catalyst as a sophomore, considering the Rebels were stricken with ACL tears. Kennedy needed his minutes, even if Graham couldn't practice. He started 23 games, the most of his career to date.
"Coming into college, I wanted to see improvement every season – freshman, sophomore, junior," Graham said. "I think with getting older, if you're not getting better and more mature – if you're doing the same things as the year before – then you're not getting better.
"I've tried to do more each year. That's what I'm going to try and do my senior year, especially with the loss of a lot of key players. I'm sure Chris and Trevor and Terrance (Henry) are going to do the same."
He was close to full health his junior season, but continued to battle nagging injuries. He made 35 appearances with 12 starts, scored nine points a game and shot 41.2 percent from the field. Graham has always sought to expand his overall play each season, with his 3-point touch the beneficiary in his third year.
He shot close to 40 percent from beyond the arc.
But his gradual improvement throughout the years has gone, for the most part, unnoticed. Ole Miss hasn't made the NCAA Tournament in eight straight seasons, three of which Graham has been a part of. None were more disappointing than 2009-10, when a talented roster again settled for an NIT berth.
"I think with the group of guys we have this year, with the guys we have coming in including the freshmen, I believe we'll have a more mature team than we had last year," he said. "We had all the talent last year. This year we have a talented team coming back. But our maturity, level of focus, attention to detail and hunger will be better this year."
He's more motivated as a senior, mainly because he's healthy. He can squat for the first time since his freshman year, and is using the offseason to get stronger in his legs, along with regular workouts to strengthen his core.
Basically, he just wants to be a better all-around player, no matter how cliché the description might sound.
"Individually, as a player, every player has that mindset," he said. "That's why you work hard in the summer, like I'm working hard now, to prepare for the season. Individually, you always want to be more productive. It will help the team out."
The lack of an NCAA Tournament appearance eats at him. He's seen some of his close friends from high school and players he once competed against play on college basketball's biggest stage. Graham, meanwhile, has only been a spectator with the rest of us.
"It's an experience not a lot of people get," he said. "That's an experience our team wants this year."
Making it in the now-expanded tournament field is what drives him, as well as the rest of the returning veterans. It's all that matters now.
"We came in with expectations," Graham said. "Since I've been here, we've done some things, but the ultimate goal is to make the NCAA Tournament. We want to get there. It's been three years. This is our last year. We've grinded out and worked hard, but have always been like one game out. Now we know what it takes. It's not easy. It's hard.
"The commitment that it takes… we want to get there. That's our goal."
Ole Miss finished 24-11 a year ago, but irritating matters on an off the court – chemistry and suspensions – disrupted a promising season from ever truly taking off.
The Rebels were ever-so-close to dancing, with a loss to Tennessee in the SEC Tournament the final break that didn't fall in Ole Miss' favor, and essentially sealed its postseason fate. Near misses isn't the legacy Graham, Warren and Gaskins want to leave.
Quite the contrary, actually.
"We want this season to say that we left with people respecting Ole Miss," he said. "We want to leave with recognition and people talking about our team. We want to be mentioned. We don't want to be the odd man out. We want to be an NCAA Tournament team."