centralgraph               package:sna               R Documentation

_F_i_n_d _t_h_e _C_e_n_t_r_a_l _G_r_a_p_h _o_f _a _L_a_b_e_l_e_d _G_r_a_p_h _S_e_t

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

     Returns the central graph of a set of labeled graphs, i.e. that
     graph in which i->j iff i->j in >=50% of the graphs within the
     set.  If `normalize==TRUE', then the value of the i,jth edge is
     given as the proportion of graphs in which i->j.

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

     centralgraph(dat, normalize=FALSE)

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

     dat: Data array to be analyzed.  By assumption, the first
          dimension of the array indexes the graph, with the next two
          indexing the actors. 

normalize: Boolean indicating whether the results should be normalized.
           The result of this is the "mean matrix".  By default,
          `normalize==FALSE'.

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

     The central graph of a set of graphs S is that graph C which
     minimizes the sum of Hamming distances between C and G in S.  As
     such, it turns out (for the dichotomous case, at least), to be
     analogous to both the mean and median for sets of graphs.  The
     central graph is useful in a variety of contexts; see the
     references below for more details.

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

     A matrix containing the central graph (or mean matrix)

_N_o_t_e:

     0.5 is used as the cutoff value regardless of whether or not the
     data is dichotomous (as is tacitly assumed).  The routine is
     unaffected by data type when `normalize==TRUE'.

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

     Carter T. Butts ctb@andrew.cmu.edu

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

     `hdist'

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

     #Generate some random graphs
     dat<-rgraph(10,5)
     #Find the central graph
     cg<-centralgraph(dat)
     #Plot the central graph
     gplot(cg)
     #Now, look at the mean matrix
     cg<-centralgraph(dat,normalize=TRUE)
     print(cg)

