transitivity             package:igraph             R Documentation

_T_r_a_n_s_i_t_i_v_i_t_y _o_f _a _g_r_a_p_h

_D_e_s_c_r_i_p_t_i_o_n:

     Transitivity measures the probability that the adjacent vertices
     of a vertex are connected. This is sometimes also called the
     clustering coefficient.

_U_s_a_g_e:

     transitivity(graph, type=c("undirected", "global", "globalundirected",
            "localundirected", "local", "average", "localaverage",
            "localaverageundirected"), vids=NULL)

_A_r_g_u_m_e_n_t_s:

   graph: The graph to analyze.

    type: The type of the transitivity to calculate. Possible values:

        '_g_l_o_b_a_l' The global transitivity of an undirected graph
             (directed graphs are considered as undirected ones as
             well). This is simply the ratio of the triangles and the
             connected triples in the graph. For directed graph the
             direction of the edges is ignored. 

        '_l_o_c_a_l' The local transitivity of an undirected graph, this is
             calculated for each vertex given in the 'vids' argument.
             The local transitivity of a vertex is the ratio of the
             triangles connected to the vertex and the triples centered
             on the vertex. For directed graph the direction of the
             edges is ignored. 

        '_u_n_d_i_r_e_c_t_e_d' This is the same as 'global'.

        '_g_l_o_b_a_l_u_n_d_i_r_e_c_t_e_d' This is the same as 'global'.

        '_l_o_c_a_l_u_n_d_i_r_e_c_t_e_d' This is the same as 'local'.

    vids: The vertex ids for the local transitivity will be calculated.
          This will be ignored for global transitivity types. The
          default value is 'NULL', in this case all vertices are
          considered. It is slightly faster to supply 'NULL' here than
          'V(graph)'. 

_V_a_l_u_e:

     For ''global'' a single number, or 'NaN' if there are no connected
     triples in the graph.

     For ''local'' a vector of transitivity scores, one for each vertex
     in ''vids''.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_R_e_f_e_r_e_n_c_e_s:

     Wasserman, S., and Faust, K. (1994). _Social Network Analysis:
     Methods and Applications._ Cambridge: Cambridge University Press.

_E_x_a_m_p_l_e_s:

     g <- graph.ring(10)
     transitivity(g)
     g2 <- erdos.renyi.game(1000, 10/1000)
     transitivity(g2)   # this is about 10/1000

