In 1972, Graham was appointed lecturer at the University of Copenhagen, where he co-founded the Centre for Medieval Studies at Copenhagen, University of Copenhagen. In 1990, he was appointed to the Chair of English Language at Glasgow University. In 2004, he was elected as a Vice President of the Royal Society of Edinburgh. He retired from the University of Glasgow, in 2012. In 2014, he became a member of the British Council’s Advisory Committee for Scotland.