triad.census             package:igraph             R Documentation

_T_r_i_a_d _c_e_n_s_u_s, _s_u_b_g_r_a_p_h_s _w_i_t_h _t_h_r_e_e _v_e_r_t_i_c_e_s

_D_e_s_c_r_i_p_t_i_o_n:

     This function counts the different subgraphs of three vertices in
     a graph.

_U_s_a_g_e:

     triad.census(graph)

_A_r_g_u_m_e_n_t_s:

   graph: The input graph, it should be directed. An undirected graph
          results a warning, and undefined results.

_D_e_t_a_i_l_s:

     Triad census was defined by David and Leinhardt (see References
     below). Every triple of vertices (A, B, C) are classified into the
     16 possible states:

   _0_0_3 A,B,C, the empty graph.

   _0_1_2 A->B, C, the graph with a single directed edge.

   _1_0_2 A<->B, C, the graph with a mutual connection between two
        vertices.

   _0_2_1_D A<-B->C, the out-star.

   _0_2_1_U A->B<-C, the in-star.

   _0_2_1_C A->B->C, directed line.

   _1_1_1_D A<->B<-C.

   _1_1_1_U A<->B->C.

   _0_3_0_T A->B<-C, A->C.

   _0_3_0_C A<-B<-C, A->C.

   _2_0_1 A<->B<->C.

   _1_2_0_D A<-B->C, A<->C.

   _1_2_0_U A->B<-C, A<->C.

   _1_2_0_C A->B->C, A<->C.

   _2_1_0 A->B<->C, A<->C.

   _3_0_0 A<->B<->C, A<->C, the complete graph.

     This functions uses the RANDESU motif finder algorithm to find and
     count the subgraphs, see 'graph.motifs'.

_V_a_l_u_e:

     A numeric vector, the subgraph counts, in the order given in the
     above description.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_R_e_f_e_r_e_n_c_e_s:

     See also Davis, J.A. and Leinhardt, S.  (1972).  The Structure of
     Positive Interpersonal Relations in Small Groups.  In J. Berger
     (Ed.), Sociological Theories in Progress, Volume 2, 218-251. 
     Boston: Houghton Mifflin.

_S_e_e _A_l_s_o:

     'dyad.census' for classifying binary relationships, 'graph.motifs'
     for the underlying implementation.

_E_x_a_m_p_l_e_s:

     g <- erdos.renyi.game(15, 45, type="gnm", dir=TRUE)
     triad.census(g)

