admittance matrix | normalized Laplacian matrix

The Laplacian matrix, sometimes also called the admittance matrix (Cvetković et al. 1998, Babić et al. 2002) or Kirchhoff matrix, of a graph G, where G = (V, E) is an undirected, unweighted graph without graph loops (i, i) or multiple edges from one node to another, V is the vertex set, n = left bracketing bar V right bracketing bar , and E is the edge set, is an n×n symmetric matrix with one row and column for each node defined by L = D - A, where D = diag(d_1, ..., d_n) is the degree matrix, which is the diagonal matrix formed from the vertex degrees and A is the adjacency matrix. The diagonal elements l_(i j) of L are therefore equal the degree of vertex v_i and off-diagonal elements l_(i j) are -1 if vertex v_i is adjacent to v_j and 0 otherwise.

algebraic connectivity | Fiedler vector | Laplacian polynomial | Laplacian spectral radius | Laplacian spectral ratio | matrix tree theorem | resistance distance | spectral graph partitioning