Graham's primary research interests are in moral psychology, which focuses on the connection between ethics and rationality.  It examines this connection in both directions: it analyzes the rationality of ethics as well as the extent to which rational standards can be evaluated ethically.  It is guided by the thought that ethics cannot be done in a cognitive and epistemic vacuum—it must be informed by, and sometimes can even inform, epistemology and the philosophy of mind. 

While Graham's research investigates our ethical lives from an individual, psychological perspective, most of his classes concern the social and political side of ethics. The goal of his teaching is to contextualize philosophical inquiry in a way that is relevant to students’ lives. In this vein, Graham leads service-learning trips to Karagwe, Tanzania through Amizade Global Service-Learning Programs.