connectedness              package:sna              R Documentation

_C_o_m_p_u_t_e _G_r_a_p_h _C_o_n_n_e_c_t_e_d_n_e_s_s _S_c_o_r_e_s

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

     'connectedness' takes a graph stack ('dat') and returns the
     Krackhardt connectedness scores for the graphs selected by 'g'.

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

     connectedness(dat, g=1:stackcount(dat))

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

     dat: A graph or graph stack 

       g: Index values for the graphs to be utilized; by default, all
          graphs are selected 

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

     Krackhardt's connectedness for a digraph G is equal to the
     fraction of all dyads, {i,j}, such that there exists an undirected
     path from i to j in G.  (This, in turn, is just the density of the
     weak 'reachability' graph of G.)  Obviously, the connectedness
     score ranges from 0 (for the null graph) to 1 (for weakly
     connected graphs).

     Connectedness is one of four measures ('connectedness',
     'efficiency', 'hierarchy', and 'lubness') suggested by Krackhardt
     for summarizing hierarchical structures.  Each corresponds to one
     of four axioms which are necessary and sufficient for the
     structure in question to be an outtree; thus, the measures will be
     equal to 1 for a given graph iff that graph is an outtree. 
     Deviations from unity can be interpreted in terms of failure to
     satisfy one or more of the outtree conditions, information which
     may be useful in classifying its structural properties.

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

     A vector containing the connectedness scores

_N_o_t_e:

     The four Krackhardt indices are, in general, nondegenerate for a
     relatively narrow band of size/density combinations (efficiency
     being the sole exception).  This is primarily due to their
     dependence on the reachability graph, which tends to become
     complete rapidly as size/density increase.  See Krackhardt (1994)
     for a useful simulation study.

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

     Carter T. Butts buttsc@uci.edu

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

     Krackhardt, David.  (1994).  ``Graph Theoretical Dimensions of
     Informal Organizations.'' In K. M. Carley and M. J. Prietula
     (Eds.), _Computational Organization Theory_, 89-111. Hillsdale,
     NJ: Lawrence Erlbaum and Associates.

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

     'connectedness', 'efficiency', 'hierarchy', 'lubness',
     'reachability'

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

     #Get connectedness scores for graphs of varying densities
     connectedness(rgraph(10,5,tprob=c(0.1,0.25,0.5,0.75,0.9)))

