### Hamiltonian pathsEdit

The following identity connects the weights of the paths of a network and its dual, an integral of conductivity over the network and the eigenvalues of the Laplacian of the dual graphs, that admit Hamiltonian paths.

The latest reviewed version was checked on *9 September 2016*. There is 1 pending change awaiting review.

The following identity connects the weights of the paths of a network and its dual, an integral of conductivity over the network and the eigenvalues of the Laplacian of the dual graphs, that admit Hamiltonian paths.

- ${\frac {\det(\Lambda (P,Q))}{\det(\Lambda ^{*}(P^{*},Q^{*}))}}=\prod _{e\in E}\gamma (e)({\frac {\det(K^{*})}{\det(K)}}).$