This result has previously been employed in nonprojective dependency parsing (Koo et al., 2007;Smith and Smith, 2007).
let l ∈ R n×n denote the laplacian of G, namely Tutte's theorem relates the determinant of the laplacian to the spanning trees in graph G. the cofactor l 0,0 equals the total weight of all directed spanning trees rooted at node 0.