Graham played college football as a defensive lineman at Yale University, graduating with a bachelor's degree in sociology in 2002.

In 2007, he was a defensive graduate assistant under head coach Charlie Weis at the University of Notre Dame.

[1] Following the 2008 season, Graham accepted the position as the team's defensive line coach at the University of Toledo.

[7] After originally being announced as being retained by Brian Daboll, on February 4, 2022, Graham was hired by the Las Vegas Raiders as defensive coordinator under new head coach Josh McDaniels.

[8] On February 1, 2024, the Raiders announced Graham would be retained under new head coach Antonio Pierce.