Editing Discrete Laplace operator (section)

==Theorems==
If the graph is an infinite [[square lattice|square lattice grid]], then this definition of the Laplacian can be shown to correspond to the continuous Laplacian in the limit of an infinitely fine grid.  Thus, for example, on a one-dimensional grid we have

:<math>\frac{\partial^2F}{\partial x^2} = 
\lim_{\epsilon \rightarrow 0} 
  \frac{[F(x+\epsilon)-F(x)]-[F(x)-F(x-\epsilon)]}{\epsilon^2}.
</math>

This definition of the Laplacian is commonly used in [[numerical analysis]] and in [[image processing]]. In image processing, it is considered to be a type of [[digital filter]], more specifically an [[edge filter]], called the [[Laplace filter]].