kleinberg               package:igraph               R Documentation

_K_l_e_i_n_b_e_r_g'_s _c_e_n_t_r_a_l_i_t_y _s_c_o_r_e_s.

_D_e_s_c_r_i_p_t_i_o_n:

     Kleinberg's hub and authority scores.

_U_s_a_g_e:

     authority.score (graph, scale = TRUE, options = igraph.arpack.default) 
     hub.score (graph, scale = TRUE, options = igraph.arpack.default) 

_A_r_g_u_m_e_n_t_s:

   graph: The input graph.

   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.

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

_D_e_t_a_i_l_s:

     The authority scores of the vertices are defined as the principal
     eigenvector of t(A)*A, where A is the adjacency matrix of the
     graph.

     The hub scores of the vertices are defined as the principal
     eigenvector of A*t(A), where A is the adjacency matrix of the
     graph.

     Obviously, for undirected matrices the adjacency matrix is
     symmetric and the two scores are the same.

_V_a_l_u_e:

     A named list with members: 

  vector: The authority/hub scores of the vertices.

   value: The corresponding eigenvalue of the calculated principal
          eigenvector.

 options: Some information about the ARPACK computation, it has the
          same members as the 'options' member returned by 'arpack',
          see that for documentation.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_R_e_f_e_r_e_n_c_e_s:

     J. Kleinberg. Authoritative sources in a hyperlinked environment.
     _Proc. 9th ACM-SIAM Symposium on Discrete Algorithms_, 1998.
     Extended version in _Journal of the ACM_ 46(1999). Also appears as
     IBM Research Report RJ 10076, May 1997.

_S_e_e _A_l_s_o:

     'evcent' for eigenvector centrality, 'page.rank' for the Page Rank
     scores. 'arpack' for the underlining machinery of the computation.

_E_x_a_m_p_l_e_s:

     ## An in-star
     g <- graph.star(10)
     hub.score(g)$vector
     authority.score(g)$vector

     ## A ring
     g2 <- graph.ring(10)
     hub.score(g2)$vector
     authority.score(g2)$vector

