The laplacian of a matrix also has cool applications in computer graphics, if anyone is curious (about further connections). Think of the mesh of an object as a graph and compute the lapacian. (You get natural unsupervised segmentations of the mesh for instance if you look at it as a spectral clustering problem.) Look up resources by Keenan Crane. If you've played with 'smooth normals' in blender I believe it uses techniques like that as well.