I am starting to learn about the laplacian operator $\Delta = \nabla \cdot \nabla\phi(p)$
Which can be described as the divergence of the gradient of a scalar function $\phi$. This is equivalent to the sum of the second order partial derivatives of the function.
However, it seems its graph equivalent is just the sum of the differences of adjacent vertices. Am I reading that right? In my head that should be equivalent to the first order partial derivatives, not the second order ones.
(I didn't know whether to ask here or in math, I decided here is more relevant because this is in the context of geometry processing)