In various papers I've been reading, the authors embed a graph in a manifold, then claim that one can approximate the discrete Laplacian with the continuous Laplacian by expanding the continuous Laplace operator up to whatever order. Then, the spectra are supposed to converge asymptotically.
Though intuitively obvious as the graph grows and the relative distance between points shrinks, I would like to see a proof and an estimate of the associated error. None of the authors cite a source, so my guess is that this must be well known.