After five professional seasons in North American, Graham opted to pursue a European career, moving to the Tipsport Liga in Slovakia to join HK Nitra on October 26, 2019.[4] but left just two weeks later after playing three games for the team to join Finnish club, KalPa of Liiga.[5]
Graham spent the duration of the 2021–22 season with Augsburger Panther of the Deutsche Eishockey Liga (DEL), contributing with 3 goals and 39 assists for 42 points in 52 games, leading the blueline in scoring.[6]
As a free agent, Graham moved to the KHL, in agreeing to a one-year contract for the 2022–23 season with Kazakh based club, Barys Nur-Sultan, on July 20, 2022.[7] In his debut KHL season, Graham was a fixture on the Barys blueline, registering 19 assists through 66 regular season games.
On May 11, 2023, Graham opted to continue his tenure in the KHL, however moved to Russian club, HC Sochi, after securing a two-year contract as a free agent.[8]