closeness                package:sna                R Documentation

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

     'closeness' takes one or more graphs ('dat') and returns the
     closeness centralities of positions (selected by 'nodes') within
     the graphs indicated by 'g'.  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=NULL, gmode="digraph", diag=FALSE, 
         tmaxdev=FALSE, cmode="directed", geodist.precomp=NULL, 
         rescale=FALSE)

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

     dat: one or more input graphs. 

       g: integer indicating the index of the graph for which
          centralities are to be calculated (or a vector thereof).  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) = (|V(G)|-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 'Inf'.  It should be
     understood that this modification is not canonical (though it is
     common), 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, matrix, or list containing the closeness scores
     (depending on the number and size of the input graphs).

_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, buttsc@uci.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

