While at Monrovia High School, he played for the football time in the halfback position from 1972 until 1974.
Graves went on to Citrus College, where he played from 1975 to 1976. While there, he earned and still holds the records for: Most Carries In A Season: (235), for the 1975 season; Most Rushing Yards In A Season (1228), for the 1976 season; Most All Purpose Yards In A Season (1445), for the 1976 season; Most Points In A Season: (108) for the 1976 season, Most Touchdowns In A Season: (18) for the 1976 season, Most Points In A Career: (138), for his career there spanning 1975-1976; and Most Touchdowns In A Career: (23) for 1975-1976.
Graves played in the Canadian Football League after he graduated from college, playing two seasons as a running back for the Hamilton Tiger-Cats, from 1980 to 1982. He holds the Tiger-Cat record for most carries in a game, with thirty-three carries.