prestige                 package:sna                 R Documentation

_C_a_l_c_u_l_a_t_e _t_h_e _V_e_r_t_e_x _P_r_e_s_t_i_g_e _S_c_o_r_e_s

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

     'prestige' takes a graph stack ('dat') and returns the prestige
     scores of positions within one graph (indicated by 'nodes' and
     'g', respectively).  Depending on the specified mode, prestige
     based on any one of a number of different definitions will be
     returned. This function is compatible with 'centralization', and
     will return the theoretical maximum absolute deviation (from
     maximum) conditional on size (which is used by 'centralization' to
     normalize the observed centralization score).

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

     prestige(dat, g=1, nodes=c(1:dim(dat)[2]), gmode="digraph", 
         diag=FALSE, cmode="indegree", tmaxdev=FALSE, rescale=FALSE, 
         tol=1e-07)

_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. Alternately, this can be an n x n matrix
          (if only one graph is involved). 

       g: Integer indicating the index of the graph for which
          centralities are to be calculated.  By default, 'g==1'. 

   nodes: List indicating which nodes are to be included in the
          calculation.  By default, all nodes are included. 

   gmode: String indicating the type of graph being evaluated. 
          "digraph" indicates that edges should be interpreted as
          directed; "graph" indicates that edges are undirected. 
          'gmode' is set to "digraph" by default.

    diag: Boolean indicating whether or not the diagonal should be
          treated as valid data.  Set this true if and only if the data
          can contain loops.  'diag' is 'FALSE' by default. 

   cmode: One of "indegree", "indegree.rownorm", "indegree.rowcolnorm",
          "eigenvector", "eigenvector.rownorm", "eigenvector.colnorm",
          "eigenvector.rowcolnorm", "domain", or "domain.proximity" 

 tmaxdev: Boolean indicating whether or not the theoretical maximum
          absolute deviation from the maximum nodal centrality should
          be returned.  By default, 'tmaxdev==FALSE'. 

 rescale: If true, centrality scores are rescaled such that they sum to
          1. 

     tol: Currently ignored 

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

     "Prestige" is the name collectively given to a range of centrality
     scores which focus on the extent to which one is nominated by
     others.  The definitions supported here are as follows:

        1.  indegree: indegree centrality

        2.  indegree.rownorm: indegree within the row-normalized graph

        3.  indegree.rowcolnorm: indegree within the row-column
           normalized graph

        4.  eigenvector: eigenvector centrality within the transposed
           graph (i.e., incoming ties recursively determine prestige)

        5.  eigenvector.rownorm: eigenvector centrality within the
           transposed row-normalized graph

        6.  eigenvector.colnorm: eigenvector centrality within the
           transposed column-normalized graph

        7.  eigenvector.rowcolnorm: eigenvector centrality within the
           transposed row/column-normalized graph

        8.  domain: indegree within the reachability graph (Lin's
           unweighted measure)

        9.  domain.proximity: Lin's proximity-weighted domain prestige

     Note that the centralization of prestige is simply the extent to
     which one actor has substantially greater prestige than others;
     the underlying definition is the same.

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

     A vector of prestige scores

_W_a_r_n_i_n_g:

     Making adjacency matrices doubly stochastic (row-column
     normalization) is not guaranteed to work.  In general, be wary of
     attempting to try normalizations on graphs with degenerate rows
     and columns.

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

     Carter T. Butts buttsc@uci.edu

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

     Lin, N.  (1976).  _Foundations of Social Research_.  New York:
     McGraw Hill.

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

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

     'centralization'

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

     g<-rgraph(10)                 #Draw a random graph with 10 members
     prestige(g,cmode="domain")    #Compute domain prestige scores

