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Questions related to the spectrum of graphs, defined using one of the possible variants of the discrete Laplace operator or Laplacian matrix. See https://en.wikipedia.org/wiki/Discrete_Laplace_operator

24 votes

Is the Laplacian on a manifold the limit of graph Laplacians?

If laplacian $\Delta_n$ is defined just as $\[\Delta_n f\](u)=\sum_v (f(v)-f(u))$, where the sum is over all neighbors v of the vertex u, then the answer is NO. Informal reason is that such $\Delta_n$ …
mikhail skopenkov's user avatar