Abstract. Graph theory provides a substantial resource for a diverse range of quantitative and qualitative usability measures that can be used for evaluating recovery from error, informing design tradeoffs, probing topics for user training, and so on.Graph theory is a straight-forward, practical and flexible way to implement real interactive systems. Hence, graph theory complements other approaches to formal HCI, such as theorem proving and model checking, which have a less direct relation to interaction. This paper gives concrete examples based on the analysis of a real non-trivial interactive device, a medical syringe pump, itself modelled as a graph. New ideas to HCI (such as small world graphs) are introduced, which may stimulate further research.