He helped Hibernian win the 2016–17 Scottish Championship, then moved to English club Cheltenham Town in August 2017.

Graham returned to Ross County in August 2018 and subsequently joined Partick Thistle in 2020, going on to become team captain and one of the club's most prolific goal-scorers.

Graham was unveiled as a Dundee United player before the SPL club's last game of the 2012–13 season against Celtic at Tannadice, signing a two-year deal as Jon Daly made an exit.

[13] He scored 11 goals in his first season at the club and started the 2016 Scottish League Cup Final victory over Hibernian, which gave County their first ever piece of silverware.

[14] Graham began the 2016–17 season in fine form, scoring in all four of Ross County's group stage matches in the reformatted League Cup.

He also netted in a 3–2 to Alloa, and despite scoring a hat-trick as County thrashed Cove Rangers 7–0 on 30 July, it proved to be not enough as the club finished third in their group and thus failed to qualify for the knockout round.

A 3–1 defeat to Dundee on the opening day of the Scottish Premiership season proved to be Graham's last match for Ross County as he was released by the club on 19 August 2016, despite having a year left on his contract.

[15] He signed for Hibernian the next day on a free transfer, although County later received a fee as Hibs gained promotion to the Premiership.

[20] Graham signed for Scottish Championship club Partick Thistle on a 2+1⁄2-year deal, knocking back offers from Premiership sides, Motherwell, Kilmarnock and St.

After winning League One with Thistle and finishing as the club's top scorer with 11 goals, Graham signed a new contract adding an extra year to his deal, extending it until 2023.