Born in Nashville, Tennessee, on June 25, 1935,[1] Graham received his BA in history from Yale University in 1957 (he also was a varsity wrestler at Yale).

After serving three years as an officer in the US Marine Corps, he earned his PhD in history at Columbia University in 1966 (under Richard Hofstadter and William Leuchtenburg)[2][citation needed] with a doctoral dissertation entitled The Old Progressive and the New Deal: A Study of the Modern Reform Tradition.

[3] He taught at Mount Vernon Seminary and College and then California State University, Hayward, before he joined the Department of History at the University of California, Santa Barbara, in 1966 (the same year as Alfred Gollin).

He returned to the history department at the University of California, Santa Barbara, in 1989 and taught there until 1995.

Graham was awarded fellowships by the John Simon Guggenheim Foundation, the Woodrow Wilson Center, the National Endowment for the Humanities, and the Center for Advanced Study in the Behavioral Sciences.