Spent his early childhood on Bedford Street in Greenwich Village. His father taught at NYU and Queens College. Graham later grew up in Lyme, Connecticut.
Appeared with his brother, political commentator Bob Beckel, on FOX's Sean Hannity on September 22, 2009. Bob is a liberal pundit and Graham is a conservative. The brothers discussed politics with Hannity.
Alumnus of the AADA (American Academy of Dramatic Arts), Class of 1972.