rguman                  package:sna                  R Documentation

_D_r_a_w _D_y_a_d _C_e_n_s_u_s-_C_o_n_d_i_t_i_o_n_e_d _R_a_n_d_o_m _G_r_a_p_h_s

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

     'rguman' generates random draws from a dyad census-conditioned
     uniform random graph distribution.

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

     rguman(n, nv, mut = 0.25, asym = 0.5, null = 0.25, 
         method = c("probability", "exact"))

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

       n: the number of graphs to generate. 

      nv: the size of the vertex set (|V(G)|) for the random graphs. 

     mut: if 'method=="probability"', the probability of obtaining a
          mutual dyad; otherwise, the number of mutual dyads. 

    asym: if 'method=="probability"', the probability of obtaining an
          asymmetric dyad; otherwise, the number of asymmetric dyads. 

    null: if 'method=="probability"', the probability of obtaining a
          null dyad; otherwise, the number of null dyads. 

  method: the generation method to use.  '"probability"' results in a
          multinomial dyad distribution (conditional on the underlying
          rates), while '"exact"' results in a uniform draw conditional
          on the exact dyad distribution. 

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

     A simple generalization of the Erd\"{o}s-R\'{e}nyi family, the
     U|MAN distributions are uniform on the set of graphs, conditional
     on order (size) and the dyad census.  As with the E-R case, there
     are two U|MAN variants.  The first (corresponding to
     'method=="probability"') takes dyad states as independent
     multinomials with parameters m (for mutuals), a (for asymmetrics),
     and n (for nulls).  The resulting pmf is then

            p(G=g|m,a,n) = (M+A+N)!/(M!A!N!) m^M a^A n^N,

     where M, A, and N are realized counts of mutual, asymmetric, and
     null dyads, respectively.  (See 'dyad.census' for an explication
     of dyad types.) 

     The second U|MAN variant is selected by 'method=="exact"', and
     places equal mass on all graphs having the specified (exact) dyad
     census.  The corresponding pmf is

                   p(G=g|M,A,N) = M!A!N!/(M+A+N)!.


     U|MAN graphs provide a natural baseline model for networks which
     are constrained by size, density, and reciprocity.  In this way,
     they provide a bridge between edgewise models (e.g., the E-R
     family) and models with higher order dependence (e.g., the Markov
     graphs).

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

     A matrix or array containing the drawn adjacency matrices

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

     Carter T. Butts buttsc@uci.edu

_R_e_f_e_r_e_n_c_e_s:

     Holland, P.W. and Leinhardt, S.  (1976).  ``Local Structure in
     Social Networks.''  In D. Heise (Ed.), _Sociological Methodology_,
     pp 1-45.  San Francisco: Jossey-Bass.

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

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

     'rgraph', 'rgnm', 'dyad.census'

_E_x_a_m_p_l_e_s:

     #Show some examples of extreme U|MAN graphs
     gplot(rguman(1,10,mut=45,asym=0,null=0,method="exact")) #Clique
     gplot(rguman(1,10,mut=0,asym=45,null=0,method="exact")) #Tournament
     gplot(rguman(1,10,mut=0,asym=0,null=45,method="exact")) #Empty

     #Draw a sample of multinomial U|MAN graphs
     g<-rguman(5,10,mut=0.15,asym=0.05,null=0.8)

     #Examine the dyad census
     dyad.census(g)

