Frederick Hartley Graham (December 11, 1900 – August 29, 1952) was an American football player. He played professionally in the National Football League (NFL) in 1926 with the Providence Steam Roller and the Frankford Yellow Jackets. Prior to joining the NFL, Graham attended and played college football at West Virginia University. At West Virginia, Graham excelled in football and basketball from 1921 to 1925 and earned first-team All-American honors in basketball in 1924. He also earned four letters in football as an end and served as the team's captain in 1924.