brandes.betweenness.centrality     package:RBGL     R Documentation

_C_o_m_p_u_t_e _b_e_t_w_e_e_n_n_e_s_s _c_e_n_t_r_a_l_i_t_y _f_o_r _a_n _u_n_d_i_r_e_c_t_e_d _g_r_a_p_h

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

     Compute betweenness centrality for an undirected graph

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

     brandes.betweenness.centrality(g)

_A_r_g_u_m_e_n_t_s:

       g: an instance of the 'graph' class with 'edgemode' "undirected"

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

     'Brandes.betweenness.centrality' computes the betweenness
     centrality of  each vertex or each edge in the graph, using an
     algorithm by U. Brandes.

     Betweenness centrality of a vertex 'v' is calculated as follows:
     'N_st(v)' = no. of shortest paths from 's' to 't' that pass
     through 'v', 'N_st' = no. of shortest paths from 's' to 't',
     betweenness centrality of 'v' = 'sum(N_st(v)/N_st)' for all
     vertices 's' != 'v' != 't'.

     Betweenness centrality of an edge is calculated similarly.

     The relative betweenness centrality for a vertex is to scale the
     betweenness centrality of the given vertex by '2/(n**2 - 3n + 2)'
     where 'n' is  the no. of vertices in the graph.

     Central point dominance measures the maximum betweenness of any
     vertex  in the graph.

     See documentation on brandes betweenness centrality in Boost Graph
     Library  for more details.

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

     A list of 

betweenness.centrality.vertices: betweenness centrality of each vertex

betweenness.centrality.edges: betweenness centrality of each edge

relative.betweenness.centrality.vertices: relative betweenness
          centrality of each vertex

dominance: maximum betweenness of any point in the graph

_A_u_t_h_o_r(_s):

     Li Long <li.long@isb-sib.ch>

_R_e_f_e_r_e_n_c_e_s:

     Boost Graph Library by Siek et al.

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

     'betweenness.centrality.clustering'

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

     coex <- fromGXL(file(system.file("XML/conn.gxl",package="RBGL")))
     coex@edgemode <- "undirected"
     brandes.betweenness.centrality(coex)

