Graham is professor of Computer Science, University of California, Berkeley (1981-present). She is the Pehong Chen Distinguished Professor of Electrical Engineering and Computer Science, 2001-2005.

Graham's honors and awards include elected membership in the National Academy of Engineering, and American Association for the Advancement of Science, Association for Computing Machinery, and American Academy of Arts and Sciences Fellow. She was the University of California Honored Woman of the CAL Community, 1995, and UC Berkeley Chancellor's Professor, 1997. She was the distinguished lecturer at: the Computer Science Department, Purdue University, 1991; the Computer Science Department, University of Arizona, 1992; the Department of EECS, Massachusetts Institute of Technology, 1993; and the Computer Science Department, University of Illinois, 1994. Dr. Graham was also a Forsythe Lecturer at Stanford University, 1993.