Graham is a former federal parliamentarian who represented the Queensland seat of Moreton in the House of Representatives from 2007 for the Australian Labor Party. He was a member of the Albanese Government prior to retiring at the 2025 election.
During his 18 years in the Commonwealth Parliament, Graham served on a range of key standing committees, including those focused on Aboriginal and Torres Strait Islander Affairs, Foreign Affairs, Education and Employment, and Human Rights.
He also served as Co-Chair of the Parliamentary Friendship Group dedicated to fighting diabetes and was the immediate past President of the Parliamentarians for Diabetes Global Network, advancing advocacy and leadership in health policy both nationally and internationally.
Before entering parliament, Graham worked as a schoolteacher, solicitor, and political staffer, including as Senior Policy Advisor to the Queensland Health Minister.