Kirchhoff's Theorem — Matrix-Tree

Count spanning trees = determinant of the reduced Laplacian (L = D − A)

Graph

Run

Speed

Result

Vertices n
3
Edges m
3
det (running)
Spanning trees

Log

Graph view

tree edge grounded vertex (deleted row/col) pivot elimination

Laplacian → reduced → elimination

Explanation

Load a graph and press Run all to build the Laplacian, ground a vertex (delete its row/column), and watch Gaussian elimination produce the spanning-tree count.