Laplacian matrix

noun

A square n×n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.

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Meanings

nounLaplacian matrix (plural Laplacian matrices)

plural Laplacian matrices

  1. graph theoryA square n×n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.

Origin

Named after Pierre-Simon, marquis de Laplace (1749 – 1827), a French scholar whose work was important to the development of mathematics, statistics, physics and astronomy.

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Cite this entry
APA

Laplacian matrix. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Laplacian%20matrix

MLA

“Laplacian matrix.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Laplacian%20matrix. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Laplacian matrix,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Laplacian%20matrix.

Source: Laplacian matrix on Wiktionary, CC BY-SA 4.0.