The mathematical tools in the emerging area of complex network analysis make possible an empirical examination of these concerns. In this talk we will present results from such an analysis. We have implemented and applied a standard algorithm for discovering clusters or communities in networks. We consider a network of courses formed by students' course selections. Two classes are linked together if there were students who took both classes. The strength of the link is related to the relative number of students in both classes. The algorithm we use for discovering clusters is non-parametric, in the sense that we do not specify the number of clusters for the algorithm to seek, nor do we use any information beyond the collective course choices of students.
Our results reveal five distinct groupings or clusters of classes. While the clusters consist of a fairly diverse set of courses, they nevertheless seem to each have a particular academic flavor. Our results are statistically significant in so far as it is astronomically unlikely that such clustering could occur if students were selecting classes at random. Nevertheless, the overall clustering effect is not extremely strong at the level of individual courses and students, and we caution against over-interpreting our results.
Although there will be some technical components in our presentation, it is intended to be accessible to all community members. There will be ample opportunity for discussion and critique.