On characteristic polynomial coefficients of the Laplace matrix of a weighted digraph and all minors theorem

The simple proof of the expression of characteristic polynomial coefficients of the Laplace matrix of a weighted digraph in the form of sum over all incoming forests is submitted. The proof is based on the Laplace matrix expression as a product of weighted incidence matrices and investigation of relations between its minors and forests, which is useful to calculate all Laplace matrix minors.