But as NFL clubs classify them, he's not a receiver, either.
In coach-speak, the New Orleans Saints star is an "F," which has, in essence, replaced the fullback in many NFL offenses. The idea is to switch out a blocker for another passing-game threat. Shifty, pint-sized slot receivers fill some of those spots, but in recent years, sturdier, basketball-player types -- who show up as "tight ends" on the roster -- have become more common.
Back in 2010, Gates became what was then the highest-paid tight end in football history, supplanting a similar "flex" type in Dallas Clark by earning an average per year north of $7 million. On Tuesday, Graham took that mantle by signing a four-year, $40 million deal that made him the eighth player at the position to eclipse the $7 million mark. The others: Gates, Vernon Davis, Jason Witten, Rob Gronkowski, Aaron Hernandez, Jermichael Finley and Jared Cook.
The common thread in that group is this: the versatility to play all over the formation, which is the key to playing the "F" spot, and create massive headaches for defensive coordinators.
So how will Graham's deal shake up the market? The truth is, it really won't -- for traditional tight ends, anyway.
"Unique players get paid elite money regardless of position," said one NFC general manager. "He's a rare player."
Over the past three years, Graham has hauled in 270 passes for 3,507 yards and 36 touchdowns, historic numbers for a tight end. But rather than keying a revolution, Graham's emergence has continued an evolution that was carried on by Gates, who is 807 receiving yards from reaching the 10,000-yard mark.
Notably, Gates is also less than 1,000 yards from topping the career total of Shannon Sharpe, who sits at second on the all-time list among tight ends behind Tony Gonzalez.
Some of the top names at the position today are, indeed, glorified receivers. Gronkowski -- a rare blocker -- would be one exception. Witten, who sits just ahead of Gates in the career receiving list with 9,799 yards and turned himself into a force in the run game as a pro, is another. Davis makes three.
The rest get by on effort. In some cases, they don't get by at all.
"Graham is a good player," said an NFC exec. "But a guy who can block, too, that's the harder thing to find. And so it's harder to value the guys who are just pass-catchers."
The top wide receivers in the NFL are, for the most part, every-down players. The more versatile tight ends are, too. Davis was in for more snaps than any other San Francisco 49ers skill player in 2013. Gronkowski led the New England Patriots' skill guys in snaps in 2011 and was on pace to do so again in 2012 before the injury bug bit him.
Graham led the Saints' skill players, too, but the difference between the three is clear. A healthy Gronkowski was playing more than 90 percent of the time for New England in 2011 and '12, while Davis was clearing 80 percent in '13. New Orleans' Swiss army knife, meanwhile, was at 66.9 percent last season. Yes, that's a high number, and it makes his production even more impressive, but it also highlights the way he needs to be spotted in certain situations. What separates Davis and a healthy Gronkowski from Graham is the way their blocking skills force opponents to stay in their base defense, which limits the way they can cover the tight end.
"The matchup problem it poses is to players who are perceivably supposed to be their equals -- the linebackers and safeties," said an AFC personnel director. "The dominant pass-catching tight end can turn that into more of a disadvantage (for the defense) than a receiver can, because he's more often facing an equally skilled player in the corner."
Conversely, tight ends who can't block can be played by the defense like a slot receiver, which is what New England did in holding Graham without a catch in Week 6 last season. The deficiency can cause further issues against teams with a super-charged pass rush, as the Saints have seen against the Rams and Seahawks; Graham was held to a total of 75 yards in three games against those two teams in 2013.
Are these problems worth dealing with? Of course. For that matter, Graham could still develop as a blocker, as others have.
But the bottom line is, he's still something of a specialty player, albeit a very talented one, which is why he was the first skill player to whom Saints coach Sean Payton has ever applied the franchise tag, and why he was rewarded at such a high level.
And these kinds of arguments won't end anytime soon. The Cleveland Browns' Jordan Cameron is another ex-college hoops player who has made a name for himself as a pass-catching tight end, and he was detached from the offensive line on 53 percent of his 2013 snaps, according to Pro Football Focus. He's entering a contract year, as is Thomas, who'd have less of an argument that he's a receiver, having played 72 percent of his '13 snaps in-line. College offenses, meanwhile, are only getting more wide open, feeding different types of athletes, such as 2014 first-rounder Eric Ebron, into the pipeline.
So while determining the value of a player like Graham is not exactly a new problem, it's something teams will have to deal with going forward -- and it's not getting any less complicated.
Follow Albert Breer on Twitter @AlbertBreer.