could someone provide me/refer me to a intuitive idea/proof behind Kirchhoff's Matrix Tree Theorem that uses as little technical details involving matrices/linear algebra as possible? I'm trying to give a group of talented high schoolers who haven't seen matrices before a sketch/cursory proof of the result, but I couldn't think of a good way to explain it.
Intuitive idea/proof behind Kirchhoff's Matrix Tree Theorem using as little matrices/linear algebra as possible?
graph theory;graphs;linear algebra