Kirchhoff's theorem for multigraphs

Statement

Kirchhoff's theorem holds for multigraphs as well; the matrix L is modified as follows:

• The entry q_i,j equals −m, where m is the number of edges between i and j;
• when counting the degree of a vertex, all loops are excluded.

Cayley's formula for a complete multigraph is mⁿ⁻¹(nⁿ⁻¹−(n−1)nⁿ⁻²) by same methods produced above, since a simple graph is a multigraph with m = 1.