As an undergraduate, Graham studied Natural Sciences at the University of Cambridge, specialising in theoretical physics, before continuing as a graduate student to do computational condensed matter physics research with Prof. Richard Needs in the Theory of Condensed Matter group in the Cavendish Laboratory.

He was appointed as a Lecturer at the University of Chester in 2015 and became a Senior Lecturer in 2019. His research involves using computational modelling to address problems in physics and engineering, ranging from atomic-scale modelling of materials and molecules to studying the performance of chemical reactors. Graham primarily teaches on the Physics and Chemical Engineering programmes. He has also taught physics in small group settings at the University of Cambridge. Before attending university, he was employed as a researcher at Shell Global Solutions, where he helped to develop computational models of lubricant performance in road cars.