degree                  package:sna                  R Documentation

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

     `Degree' takes a graph stack (`dat') and returns the degree
     centralities of positions within one graph (indicated by `nodes'
     and `g', respectively).  Depending on the specified mode,
     indegree, outdegree, or total (Freeman) degree 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:

     degree(dat, g=1, nodes=c(1:dim(dat)[2]), gmode="digraph", diag=FALSE,
         tmaxdev=FALSE, cmode="freeman", 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.  Provided that `FUN' is well-behaved,
          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 degree centrality being
          computed.  "indegree", "outdegree", and "freeman" refer to
          the indegree, outdegree, and total (Freeman) degree measures,
          respectively.  The default for `cmode' is "freeman". 

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

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

     Degree centrality is the social networker's term for various
     permutations of the graph theoretic notion of vertex degree:
     indegree of a vertex, v, corresponds to the cardinality of the
     vertex set N^+(v) = {i in V(G) : (i,v) in E(G)}; outdegree
     corresponds to the cardinality of the vertex set N^-(v) = {i in
     V(G) : (v,i) in E(G)}; and total (or "Freeman") degree corresponds
     to |N^+(v)|+|N^-(v)|.  (Note that, for simple graphs,
     indegree=outdegree=total degree/2.)  Obviously, degree centrality
     can be interpreted in terms of the sizes of actors' neighborhoods
     within the larger structure.  See the references below for more
     details.

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

     A vector containing the degree centrality scores

_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:

     #Create a random directed graph
     dat<-rgraph(10)
     #Find the indegrees, outdegrees, and total degrees
     degree(dat,cmode="indegree")
     degree(dat,cmode="outdegree")
     degree(dat)

