Graham has worked at Cancer Council Victoria since 1983. He has professorial appointments at The University of Melbourne and Monash University. He has over 35 years of experience in cancer epidemiology research. He founded the Melbourne Collaborative Cohort Study with which he has been able to develop his interests in the epidemiology of cancers of the breast, prostate, and colorectal cancers focusing on lifestyle and dietary factors and genetics. He also co-founded, with Professor John Hopper, large case-control-family studies of breast, prostate and colorectal cancer which now form the basis of the PEDIGREE consortium, focusing on cancer genetics.