iassortativity           package:inetwork           R Documentation

_A_s_s_o_r_t_a_t_i_v_e _M_i_x_i_n_g_s

_D_e_s_c_r_i_p_t_i_o_n:

     The function calculates the assortative mixing of each vertex in
     an undirected, unweighted graph (or network)

_U_s_a_g_e:

     iassortativity(A)

_A_r_g_u_m_e_n_t_s:

       A: a symmetric adjacency matrix with elements zeros or ones
          representing an undirected and unweighted network 

_D_e_t_a_i_l_s:

     Assortative mixing knn_i of vertex i sums the degrees of its
     neighboring vertices. The summation is then normalized to the
     vertex's  degree:

                    knn_i=(1/k_i)(sum_j A_ij*k_j)

     where k_j is the degree of vertex j and A_ij the adjacency matrix
     of the network. A scatter plot of knn versus k shows if hub (i.e.
     high-degree) vertices tend to attach to other hub vertices.

_V_a_l_u_e:

    knn : an array holding the assortative mixing of each vertex 

   Knnk : the average knn of the vertices having the same degree k. An
          increasing Knnk with k indicates that the network is
          assortative characteristic of social networks. Most nonsocial
          networks such as technological and biological networks show
          disassortativity. 

_A_u_t_h_o_r(_s):

     Sun-Chong Wang

_S_e_e _A_l_s_o:

     'itransitivity'

