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Discrete Laplace operator
The discrete Laplace operator is a linear operator, usually a matrix, that plays the role of the Laplacian on graphs and grids, encoding connectivity and approximating partial differential equations.
Laplacian matrix
The Laplacian matrix, also called the graph Laplacian or Kirchhoff matrix, is a graph matrix L = D − A whose eigenvalues reveal connectivity, spanning trees, and clustering.