spectral graph theory involves the study of graph properties that are related to the eigenvalues of various matrices, such as the adjacency matrix, the combinatorial laplacian, and the normalized laplacian. we will also discuss connection graphs, which are weighted simple graphs for which each edge is associated with a rotation matrix. connection graphs have been studied recently in a variety of areas that involve high dimensional data sets. we will describe higher dimensional versions of the adjacency, laplacian, and normalized laplacian matrices, and what their eigenvalues tell us about the connection graph.