Graham is the Pehong Chen Distinguished Professor of Electrical Engineering and Computer Science, Emerita. She has been on the Computer Science faculty at the University of California, Berkeley since 1971. She received an A.B. in mathematics from Harvard University and M.S. and Ph.D. degrees in computer science from Stanford University.

Graham's honors and awards include elected membership in the National Academy of Engineering, and the American Academy of Arts and Sciences. She is a Fellow of the American Association for the Advancement of Science and the Association for Computing Machinery. She has received the ACM SIGPLAN Career Programming Language Achievement Award (2000), the ACM Distinguished Service Award (2006), the Harvard Medal (2008), the IEEE von Neumann Medal (2009), and the Berkeley Citation (2009). She was named a University of California Honored Woman of the CAL Community in 1995.

Graham has served on numerous advisory committees; among them, the U.S. President's Information Technology Advisory Committee (PITAC). She served as the Chief Computer Scientist for the NSF-sponsored National Partnership for Advanced Computational Infrastructure (NPACI) from 1997 to 2005. She co-chaired a National Research Council study on the Future of Supercomputing. She was a member of the Harvard Board of Overseers from 2001 to 2007 and was President in 2006-2007. She currently serves as Vice-chair of the Council of the NSF-sponsored Computing Community Consortium, as the Vice-chair and Treasurer of the Board of Trustees of Cal Performances, and as a member of the Harvard Corporation.