itransitivity            package:inetwork            R Documentation

_C_l_u_s_t_e_r_i_n_g _C_o_e_f_f_i_c_i_e_n_t

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

     The clustering coefficient of each vertex of an undirected and
     unweighted network is calculated given the network's adjacency
     matrix

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

     itransitivity(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:

     The clustering coefficient or transitivity c_i of vertex i is
     defined as

            c_i = (1/(k_i(k_i-1))) sum_jh (A_ij*A_ih*A_jh)

     where k_i is the degree of vertex i and A_ij the adjacency matrix
     of the network. The clustering coefficient measures the
     connectivity of the neighboring vertices of a vertex. A decreasing
     c with k indicates that the network is hierarchical as observed in
     many nonrandom networks.

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

      c : an array holding the clustering coefficients of the vertices 

     Ck : the averaged c's for the vertices having the same degree k

_N_o_t_e:

     For large networks consisting of 700 vertices, the calculation can
     take ten minutes. The computation time/resource scales as O(n^3).

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

     Sun-Chong Wang

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

     'iassortativity'

