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 ctb@andrew.cmu.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

