Graham attempted to win a seat in the Canadian House of Commons in the 1958 election from Nova Scotia, but was defeated in the attempt. In 1972, he was appointed to the Senate of Canada by Pierre Trudeau. Graham served as president of the Liberal Party of Canada from 1976 until 1980. In 1995, he became deputy government leader in the Senate, and was promoted to Leader of the Government in the Senate in 1997, joining the Cabinet as Nova Scotia's sole representative. The Liberals had lost all of its seats in the province in the 1997 election. He served in Cabinet until 1999 when Chrétien replaced him with Bernie Boudreau in the hope that appointing Boudreau to the Senate would help him win a seat in the 2000 election.
|26th Ministry – Cabinet of Jean Chrétien|
|Cabinet Post (1)|
|Joyce Fairbairn||Leader of the Government in the Senate
|Party political offices|
|President of the Liberal Party of Canada