Spring term of 2005, three Web-assisted undergraduate mathematics courses were taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers 1; Math 236 Mathematics for Elementary Teachers II; and Math 391 Modern Geometry. While the content of these courses differ, they share common goals: to foster a deep understanding of critical mathematical content; to train students in the use of computer-based modeling and analysis technologies; and to promote the development of mathematical communication and collaboration concepts, skills, and dispositions. Outside of regular class periods, students participated in an ongoing asynchronous mathematical dialogue using the "Idaho Virtual Campus" Discussion Tool. The structure of this dialogue was analyzed using graph theoretic methods associated with social network analysis. These findings were compared to student achievement data and the results used to answer the question, "In Web-assisted undergraduate mathematics courses, how is the structure of asynchronous communication related to student achievement?" (Contains 8 tables and 3 figures.)