Laplacian matrix

English

Etymology

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.

Noun

Laplacian matrix (plural Laplacian matrices)

1. (graph theory) A square $n\times n$ 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.