Graham graduated from the University of Adelaide with a law degree and an economics degree in 1971. He commenced legal practice with the legal firm Kelly & Co in 1972 and was a partner of the firm from 1972 to 1997. During this time Graham was head of the firm’s banking and finance division. Graham was Practice Chairman of Kelly &Co between 1988 and 1997.
In 1997, Graham retired from legal practice to pursue private business interests. In partnership, Graham has grown Eureka Group, a business which operates and owns 20 hotels in Queensland and South Australia, as well as Living Choice Ltd, the largest privately owned retirement village business in Australia.