Graham is Professor of Politics, and Director of the Centre for the Study of Democracy, at the University of Westminster. He is a specialist in democratic theory and practice, with particular expertise in democratic innovations – new forms of participation in political decision-making.

Graham's publications include Democratic Innovations: Designing Institutions for Citizen Participation (Cambridge, 2009) and Can Democracy Safeguard the Future? (Polity, 2021). He was one of the organisers of the Citizens’ Assembly on Brexit, which proved influential in the development of citizens’ assemblies in the UK.

Graham is an investigator on a number of international research projects on democratic engagement, including Participedia, a global knowledge platform on participatory governance, and Scholio, which tests argument visualisation platforms with a view to improving public discourse on online news comments.

Graham is also Chair of the Foundation for Democracy and Sustainable Development.