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)

