One cool application of the discrete laplace operator is that we can use it to calculate the number of spanning trees of the graph by considering the determinan

One cool application of the discrete laplace operator is that we can use it to calculate the number of spanning trees of the graph by considering the determinants of the submatrices we get my removing 1 row and 1 column from the matrix! https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem https://en.wikipedia.org/wiki/Kirchhoff%27s_theorem