  The spectrum of the Laplacian of successive Barycentric subdivisions of a
graph converges exponentially fast to a limit which only depends on the clique
number of the initial graph and not on the graph itself. The proof uses an
explicit linear operator mapping the clique vector of a graph to the clique
vector of the Barycentric refinement. The eigenvectors of its transpose produce
integral geometric invariants for which Euler characteristic is one example.
