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"), open="r"))
     coex <- ugraph(coex)
     brandes.betweenness.centrality(coex)

