closeness                package:sna                R Documentation

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

     `closeness' takes a graph stack (`dat') and returns the closeness
     centralities of positions within one graph (indicated by `nodes'
     and `g', respectively).  Depending on the specified mode,
     closeness on directed or undirected geodesics 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:

     closeness(dat, g=1, nodes=c(1:dim(dat)[2]), gmode="digraph", 
         diag=FALSE, tmaxdev=FALSE, cmode="directed", 
         geodist.precomp=NULL, rescale=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. 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. 

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

   cmode: String indicating the type of closeness centrality being
          computed (distances on directed or undirected geodesics). 

geodist.precomp: A `geodist' object precomputed for the graph to be
          analyzed (optional) 

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

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

     The closeness of a vertex v is defined as


              C_C(v) = 1/sum( d(v,i), i in V(G), i!=v )


     where d(i,j) is the geodesic distance between i and j (where
     defined).  Closeness is ill-defined on disconnected graphs; in
     such cases, this routine substitutes a number one greater than the
     maximum path length (i.e., |V(G)|) for the geodesic distance).  It
     should be understood that this modification is not canonical, but
     can be avoided by not attempting to measure closeness on
     disconnected graphs in the first place!  Intuitively, closeness
     provides an index of the extent to which a given vertex has short
     paths to all other vertices in the graph; this is one reasonable
     measure of the extent to which a vertex is in the ``middle'' of a
     given structure.

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

     A vector containing the closeness scores.

_N_o_t_e:

     Judicious use of `geodist.precomp' can save a great deal of time
     when computing multiple path-based indices on the same network.

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

     Carter T. Butts, ctb@andrew.cmu.edu

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

     Freeman, L.C.  (1979).  ``Centrality in Social Networks I:
     Conceptual Clarification.'' Social Networks, 1, 215-239.

_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
     closeness(g)      #Compute closeness scores

