Graham is a practicing solicitor and for 28 years was a partner in global law firm Baker & McKenzie. He is currently a director of Vision Super Pty Ltd, Chair of the Western Bulldogs Ethics & Integrity Committee.

Previously Graham was a director of the Western Bulldogs Football Club, The VFL Board, AFL Appeals Board and disciplinary Tribunal. He has also been Chair of AMES Australia and the Victorian Employers Chamber of Commerce & Industry and the Melbourne Chamber of Commerce. And a member of the Board of Trustee of the Lizard Island Reef Research Foundation. He is a resident of Red Hill and a member of the Committee of the Balnarring Picnic Racing Club.