Editing Discrete Laplace operator (section)

{{Short description|Analog of the continuous Laplace operator}}
{{For|the discrete equivalent of the Laplace transform|Z-transform}}
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In mathematics, the '''discrete Laplace operator''' is an analog of the continuous [[Laplace operator]], defined so that it has meaning on a [[Graph (discrete mathematics)|graph]] or a [[lattice (group)|discrete grid]]. For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the [[Laplacian matrix]].

The discrete Laplace operator occurs in physics problems such as the [[Ising model]] and [[loop quantum gravity]], as well as in the study of discrete [[dynamical system]]s. It is also used in [[numerical analysis]] as a stand-in for the continuous Laplace operator. Common applications include [[image processing]],<ref>{{Cite web|url=https://courses.cs.washington.edu/courses/cse457/11au/lectures/image-processing.pdf|title=Image processing|last=Leventhal|first=Daniel|date=Autumn 2011|website=University of Washington|access-date=2019-12-01}}</ref> where it is known as the '''Laplace filter''', and in machine learning for [[cluster analysis|clustering]] and [[semi-supervised learning]] on neighborhood graphs.