graph.laplacian            package:igraph            R Documentation

_G_r_a_p_h _L_a_p_l_a_c_i_a_n

_D_e_s_c_r_i_p_t_i_o_n:

     The Laplacian of a graph.

_U_s_a_g_e:

     graph.laplacian(graph, normalized=FALSE)

_A_r_g_u_m_e_n_t_s:

   graph: The input graph.

normalized: Whether to calculate the normalized Laplacian. See
          definitions below.

_D_e_t_a_i_l_s:

     The Laplacian Matrix of a graph is a symmetric matrix having the
     same number of rows and columns as the number of vertices in the
     graph and element (i,j) is d[i], the degree of vertex i if if
     i==j, -1 if i!=j and there is an edge between vertices i and j and
     0 otherwise.

     A normalized version of the Laplacian Matrix is similar: element
     (i,j) is 1 if i==j, -1/sqrt(d[i] d[j]) if i!=j and there is an
     edge between vertices i and j and 0 otherwise.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_E_x_a_m_p_l_e_s:

     g <- graph.ring(10)
     graph.laplacian(g)
     graph.laplacian(g, norm=TRUE)

