Kirchhoff's theorem
(重定向自Matrix tree theorem)

In the mathematical field of graph theory Kirchhoff's theorem or Kirchhoff's matrix tree theorem named after Gustav Kirchhoff is a theorem about the number of spanning trees in a graph, showing that this number can be computed in polynomial time as the determinant of a matrix derived from the graph. It is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph.