[1] Having been a Scottish Rugby Academy stage 2 player, in 2017 Graham was signed by Edinburgh on a two year professional contract.
In August 2017 Gregor Townsend called Graham up to the extended Scotland national team training squad.
[5] His first international try came in the 2019 Six Nations match against Wales at Murrayfield,[6] and he subsequently scored two tries against England in the Calcutta Cup.
[9] Graham scored four tries in Scotland's 2024 autumn nations series fixture against Fiji as they went on to win 57-17, a game in which he also won player of the match.
During the game, he had briefly become Scotland's joint all time leading try-scorer before Duhan van der Merwe pulled ahead again before the final whistle.