Born in Harbor City, California, on April 15, 1950, Graham joined the Broncos in 1972 as a fourth-round pick from Oregon. He had a stellar career with the Ducks, earning honorable-mention All-America honors and eventually earning selection into the school's athletic hall of fame in 2001.
A part of John Ralston's first draft class as Broncos head coach and general manager, Graham became a starter six games into his rookie season, and helped the Broncos to a 30-23 upset of Oakland in his first career start.
One year later, Graham started every game during the 1973 season that saw the Broncos break through for their first winning campaign, finishing 7-5-2.