Graham was raised in the Castlemilk district of Glasgow. One of 11 siblings, he attended St Margaret Mary's Secondary School and supported Celtic as a child. Ray Houghton, who would also become an international footballer, was a downstairs neighbour in the same tenement block. After a short spell in the Junior grade with Cambuslang Rangers, in 1970 he was signed by Aberdeen and played in five league matches during his first season with the club. Despite his inexperience, he was given a place in the starting line-up for the 1970 Scottish Cup Final by manager Eddie Turnbull. Aberdeen defeated Celtic 3–1 with 17-year-old Graham making two assists via left-wing crosses. He remained at Aberdeen until July 1977, winning the Scottish League Cup in his final season. He played a total of 298 matches for The Dons, scoring 45 goals. He joined Leeds United for £125,000 at the start of the 1977–78 season. He scored a total of 47 goals in 260 appearances for Leeds over six seasons, including a hat-trick against Birmingham on 14 January 1978 - the first hat-trick to be scored by a Leeds United player in any competition for nearly five years. However, Leeds were relegated to the Second Division in the 1981–82 season and failed to regain their status in the top flight in 1982–83. Graham was subsequently sold to Manchester United for £45,000 in August 1983. He remained at Old Trafford for two seasons, scoring seven goals in 52 appearances in all competitions, before finishing his career at Bradford City where he remained until 1987.
International career
Having been capped at under-23 level at Aberdeen, Graham's international career seemed to be over prematurely when he was one of a group of squad players 'banned for life' after an incident in Copenhagen in 1975. He was later reprieved, and won a total of 11 full international caps for Scotland while playing for Leeds, making his debut against East Germany in 1977. He scored twice at international level, against Argentina and Northern Ireland – both in 1979.
Graham is frequently mentioned in the letters page of the comic Viz. In every edition, there will be a recommendation from a 'reader' that Graham is the only man to be considered for a range of positions. Graham has been recommended for a host of unlikely positions, such as taking over from Jeremy Clarkson as host of Top Gear, mediating peace negotiations between Russia and Ukraine, taking the editor's position at the London Evening Standard ahead of George Osborne, and presenting The Great British Bake Off.
