Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the structure of lectures. In this paper, we apply ideas from narrative analysis to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture as consisting of collections of narratives, to identify connections between the narratives, and to use the narrative structure to identify key features of the lecture. By looking at repetitions of the mathematical concepts across the narratives, graph theory tools provide a means of examining the structure of the lecture. The analysis highlights the demands that students may face to understand the connections between the various mathematical ideas that the instructor introduces. [For the complete proceedings, see ED583989.]