lambdaSets               package:RBGL               R Documentation

_F_i_n_d _a_l_l _t_h_e _l_a_m_b_d_a-_s_e_t_s _i_n _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:

     Find all the lambda-sets in an undirected graph

_U_s_a_g_e:

     lambdaSets(g)

_A_r_g_u_m_e_n_t_s:

       g: an instance of the 'graph' class 

_D_e_t_a_i_l_s:

     From reference (1), p. 270: A set of nodes is a lambda-set if any
     pair of nodes in the lambda set has  larger edge connectivity than
     any pair of nodes consisting of one node from  within the lamda
     set and a second node from outside the lamda set.

     As stated in reference (2), a lambda set is a maximal subset of
     nodes who have  more edge-independent paths connecting them to
     each other than to outsiders.

     A lambda set could be characterized by the minimum edge
     connectivity 'k' among its members, and could be called 'lambda-k'
     sets.

     Let N be maximum edge connectivity of graph 'g', we output all the
     lambda-k set for all k = 1, ..., N.

_V_a_l_u_e:

     Maximum edge connectivity, 'N', of the graph 'g', and A list of
     length N; k-th entry (k = 1, ..., N) is a list of all the lambda-k
      sets in graph 'g'.

_A_u_t_h_o_r(_s):

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

_R_e_f_e_r_e_n_c_e_s:

     (1) Social Network Analysis: Methods and Applications.  By S.
     Wasserman and K. Faust, pp. 269.  (2) LS sets, lambda sets and
     other cohesive subsets.  By S. P. Borgatti, M. G. Everett, P. R.
     Shirey, Social Networks 12 (1990) p. 337-357

_S_e_e _A_l_s_o:

_E_x_a_m_p_l_e_s:

     coex <- fromGXL(file(system.file("XML/snalambdaex.gxl",package="RBGL")))
     lambdaSets(coex)

