centralization              package:sna              R Documentation

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

     'Centralization' returns the centralization GLI (graph-level
     index) for a given graph in 'dat', given a (node) centrality
     measure 'FUN'.  'Centralization' follows Freeman's (1979)
     generalized definition of network centralization, and can be used
     with any properly defined centrality measure.  This measure must
     be implemented separately; see the references below for examples.

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

     centralization(dat, FUN, g=1, mode="digraph", diag=FALSE, 
         normalize=TRUE, ...)

_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.  Provided that 'FUN' is well-behaved,
          this can be an n x n matrix if only one graph is involved. 

     FUN: Function to return nodal centrality scores.

       g: Integer indicating the index of the graph for which
          centralization should be computed.  By default, 'g'=1. 

    mode: String indicating the type of graph being evaluated. 
          "digraph" indicates that edges should be interpreted as
          directed; "graph" indicates that edges are undirected. 
          'mode' 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. 

normalize: Boolean indicating whether or not the centralization score
          should be normalized to the theoretical maximum.  (Note that
          this function relies on 'FUN' to return this value when
          called with 'tmaxdev==TRUE'.)  By default, 'tmaxdev==TRUE'. 

     ...: Additional arguments to 'FUN'. 

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

     The centralization of a graph G for centrality measure C(v) is
     defined (as per Freeman (1979)) to be:


             C^*(G) = sum( |max(C(v))-C(i)|, i in V(G) )


     Or, equivalently, the absolute deviation from the maximum of C on
     G.  Generally, this value is normalized by the theoretical maximum
     centralization score, conditional on |V(G)|.  (Here, this
     functionality is activated by 'normalize'.)  'Centralization'
     depends on the function specified by 'FUN' to return the vector of
     nodal centralities when called with 'dat' and 'g', and to return
     the theoretical maximum value when called with the above and
     'tmaxdev==TRUE'.  For an example of such a centrality routine, see
     'degree'.

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

     The centralization of the specified graph.

_N_o_t_e:

     See 'cugtest' for null hypothesis tests involving centralization
     scores.

_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.

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

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

     'cugtest'

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

     #Generate some random graphs
     dat<-rgraph(5,10)
     #How centralized is the third one on indegree?
     centralization(dat,g=3,degree,cmode="indegree")
     #How about on total (Freeman) degree?
     centralization(dat,g=3,degree)

