Eigenvalues of Laplacians on a closed Riemannian manifold and its nets

We show that the eigenvalues of the Laplacian of a closed manifold M is approximated in a certain sense by the eigenvalues of the Laplacian of the graph of a 1 n 1/n -net in M as n → ∞ n → ∞ . Our approximation needs no assumption on M except for dimension.