Laplacian Matrix.

Let G be a graph with V(G) = {1;…,n} and E(G) = {e₁,…,e_m}. The Laplacian matrix of G, denoted by L(G), is the n×n matrix defined as follows. The rows and columns of L(G) are indexed by V(G). If i ≠ j then the (i, j)-entry of L(G) is 0 if vertex i and j are not adjacent, and it is -1 if i and j are adjacent. The (i, i)-entry of L(G) is d_i, the degree of the vertex i, i = 1;2,…,n. [ABSTRACT FROM AUTHOR]