%0 Journal Article %1 4389477 %A Spielman, D.A. %D 2007 %J Foundations of Computer Science, 2007. FOCS '07. 48th Annual IEEE Symposium on %K graph spectral theory %P 29-38 %T Spectral Graph Theory and its Applications %X Spectral graph theory is the study of the eigenvalues and eigenvectors of matrices associated with graphs. In this tutorial, we will try to provide some intuition as to why these eigenvectors and eigenvalues have combinatorial significance, and will sitn'ey some of their applications.