betweenness              package:igraph              R Documentation

_V_e_r_t_e_x _a_n_d _e_d_g_e _b_e_t_w_e_e_n_n_e_s_s _c_e_n_t_r_a_l_i_t_y

_D_e_s_c_r_i_p_t_i_o_n:

     The vertex and edge betweenness are (roughly) defined by the
     number of geodesics (shortest paths) going through a vertex or an
     edge.

_U_s_a_g_e:

     betweenness(graph, v=V(graph), directed = TRUE, verbose = igraph.par("verbose"))
     edge.betweenness(graph, e=E(graph), directed = TRUE)
     betweenness.estimate(graph, vids = V(graph), directed = TRUE, cutoff,
          verbose = igraph.par("verbose"))
     edge.betweenness.estimate(graph, directed = TRUE, cutoff)

_A_r_g_u_m_e_n_t_s:

   graph: The graph to analyze.

       v: The vertices for which the vertex betweenness will be
          calculated.

       e: The edges for which the edge betweenness will be calculated.

directed: Logical, whether directed paths should be considered while
          determining the shortest paths.

 verbose: Logical, whether to show a progress bar.

    vids: The vertices for which the vertex betweenness estimation will
          be calculated.

  cutoff: The maximum path length to consider when calculating the
          betweenness. If zero or negative then there is no such limit.

_D_e_t_a_i_l_s:

     The vertex betweenness of vertex 'v' is defined by


                  sum( g_ivj / g_ij, i!=j,i!=v,j!=v)


     The edge betweenness of edge 'e' is defined by


                       sum( g_iej / g_ij, i!=j)

     .

     'betweenness' calculates vertex betweenness, 'edge.betweenness'
     calculates edge.betweenness.

     'betweenness.estimate' only considers paths of length 'cutoff' or
     smaller, this can be run for larger graphs, as the running time is
     not quadratic (if 'cutoff' is small). If 'cutoff' is zero or
     negative then the function calculates the exact betweenness
     scores.

     'edge.betweenness.estimate' is similar, but for edges.

     For calculating the betweenness a similar algorithm to the one
     proposed by Brandes (see References) is used.

_V_a_l_u_e:

     A numeric vector with the betweenness score for each vertex in 'v'
     for 'betweenness'.

     A numeric vector with the edge betweenness score for each edge in
     'e' for 'edge.betweenness'.

     'betweenness.estimate' returns the estimated betweenness scores
     for vertices in 'vids', 'edge.betweenness.estimate' the estimated
     edge betweenness score for _all_ edges; both in a numeric vector.

_N_o_t_e:

     'edge.betweenness' might give false values for graphs with
     multiple edges.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_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.

     Ulrik Brandes, A Faster Algorithm for Betweenness Centrality.
     _Journal of Mathematical Sociology_ 25(2):163-177, 2001.

_S_e_e _A_l_s_o:

     'closeness', 'degree'

_E_x_a_m_p_l_e_s:

     g <- random.graph.game(10, 3/10)
     betweenness(g)
     edge.betweenness(g)

