Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the general structure of lectures. In this paper, we adapt ideas from narrative analysis and apply them 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. In particular, we use the idea of framing and embedded narratives to identify central ideas in the lecture and to understand how examples, diagrams, and smaller claims contribute to the development of those ideas. Additionally, we create a graph structure for the lecture using the repetition of mathematical ideas across embedded narratives, and we employ graph-theoretic analysis to support our identification of framing narratives and to highlight particular roles of embedded narratives.