A Short Course in Spectral Graph Theory

Prof. Steve Butler
Morrill Professor of Mathematics
Iowa State University

Graphs are used to model relationships (edges) between objects (vertices). A graph’s structure can efficiently stored in an array format. We can go one step further and replace arrays by matrices (which are arrays with benefits!), the eigenvalues of these matrices tell us some information about the graph. The extent to which we can understand the structure of the graph from these eigenvalues is spectral graph theory. We will do a quick walk through of some of the flavors of matrices that are studied in spectral graph theory, and some results that arise from their study.