Graph Laplacians constructed from a smooth nondegenerate symmetric divergence D on a compact Riemannian manifold converge pointwise to the Laplace–Beltrami operator under a fourth-order closeness condition to squared geodesic distance.
Amari.Information geometry and its applications, volume 194
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On the convergence of graph Laplacians with a symmetric divergence
Graph Laplacians constructed from a smooth nondegenerate symmetric divergence D on a compact Riemannian manifold converge pointwise to the Laplace–Beltrami operator under a fourth-order closeness condition to squared geodesic distance.