evcent                package:igraph                R Documentation

_F_i_n_d _E_i_g_e_n_v_e_c_t_o_r _C_e_n_t_r_a_l_i_t_y _S_c_o_r_e_s _o_f _N_e_t_w_o_r_k _P_o_s_i_t_i_o_n_s

_D_e_s_c_r_i_p_t_i_o_n:

     'evcent' takes a graph ('graph') and returns the eigenvector
     centralities of positions 'v' within it

_U_s_a_g_e:

     evcent (graph, scale = TRUE, weights = NULL, options = igraph.arpack.default) 

_A_r_g_u_m_e_n_t_s:

   graph: Graph to be analyzed.

   scale: Logical scalar, whether to scale the result to have a maximum
          score of one. If no scaling is used then the result vector
          has unit length in the Euclidean norm.

 weights: A numerical vector or 'NULL'. This argument can be used to
          give edge weights for calculating the weighted eigenvector
          centrality of vertices. If this is 'NULL' and the graph has a
          'weight' edge attribute then that is used. If 'weights' is a
          numerical vector then it used, even if the graph has a
          'weights' edge attribute. If this is 'NA', then no edge
          weights are used (even if the graph has a 'weight' edge
          attribute.

 options: A named list, to override some ARPACK options. See 'arpack'
          for details.

_D_e_t_a_i_l_s:

     Eigenvector centrality scores correspond to the values of the
     first eigenvector of the graph adjacency matrix; these scores may,
     in turn, be interpreted as arising from a reciprocal process in
     which the centrality of each actor is proportional to the sum of
     the centralities of those actors to whom he or she is connected. 
     In general, vertices with high eigenvector centralities are those
     which are connected to many other vertices which are, in turn,
     connected to many others (and so on).  (The perceptive may realize
     that this implies that the largest values will be obtained by
     individuals in large cliques (or high-density substructures). 
     This is also intelligible from an algebraic point of view, with
     the first eigenvector being closely related to the best rank-1
     approximation of the adjacency matrix (a relationship which is
     easy to see in the special case of a diagonalizable symmetric real
     matrix via the $S Lambda S^{-1}$ decomposition).)

     From igraph version 0.5 this function uses ARPACK for the
     underlying computation, see 'arpack' for more about ARPACK in
     igraph.

_V_a_l_u_e:

     A named list with components: 

  vector: A vector containing the centrality scores.

   value: The eigenvalue corresponding to the calculated eigenvector,
          i.e. the centrality scores.

 options: A named list, information about the underlying ARPACK
          computation. See 'arpack' for the details. 

_W_A_R_N_I_N_G:

     'evcent' will not symmetrize your data before extracting
     eigenvectors; don't send this routine asymmetric matrices unless
     you really mean to do so.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu and Carter T. Butts
     buttsc@uci.edu for the manual page

_R_e_f_e_r_e_n_c_e_s:

     Bonacich, P.  (1987).  Power and Centrality: A Family of Measures.
     _American Journal of Sociology_, 92, 1170-1182. 

     Katz, L.  (1953).  A New Status Index Derived from Sociometric
     Analysis.  _Psychometrika_, 18, 39-43.

_E_x_a_m_p_l_e_s:

     #Generate some test data
     g <- graph.ring(10, directed=FALSE)
     #Compute eigenvector centrality scores
     evcent(g)

