The Laplacian matrix is a modified form of the adjacency matrix that incorporates information about the degrees of the vertices .
Is useful in some calculations such as Kirchhoff 's theorem on the number of spanning trees of a graph .
The Laplacian matrix is a modified form of the adjacency matrix that incorporates information about the degrees of the vertices , and is useful in some calculations such as Kirchhoff 's theorem on the number of spanning trees of a graph .