Slightly better explanation: https://web.archive.org/web/20141114091039/http://math.iit.e...

You still have to figure out their convention for the matrices they're taking eigenvalues of though. Looking at the eigenvalues for K8, it seems to me that their adjacency matrices have 1 on the diagonal, and -1/n wherever there is an edge (n being the degree of the vertex), so that each row sums to 0.