cliques                package:igraph                R Documentation

_T_h_e _f_u_n_c_t_i_o_n_s _f_i_n_d _c_l_i_q_u_e_s, _i_e. _c_o_m_p_l_e_t_e _s_u_b_g_r_a_p_h_s _i_n _a _g_r_a_p_h

_D_e_s_c_r_i_p_t_i_o_n:

     These functions find all, the largest or all the maximal cliques
     in an undirected graph. The size of the largest clique can also be
     calculated.

_U_s_a_g_e:

     cliques(graph, min=NULL, max=NULL)
     largest.cliques(graph)
     maximal.cliques(graph)
     clique.number(graph)

_A_r_g_u_m_e_n_t_s:

   graph: The input graph, directed graphs will be considered as
          undirected ones, multiple edges and loops are ignored.

     min: Numeric constant, lower limit on the size of the cliques to
          find. 'NULL' means no limit, ie. it is the same as 0.

     max: Numeric constant, upper limit on the size of the cliques to
          find. 'NULL' means no limit.

_D_e_t_a_i_l_s:

     'cliques' find all complete subgraphs in the input graph, obeying
     the size limitations given in the 'min' and 'max' arguments.

     'largest.cliques' finds all largest cliques in the input graph. A
     clique is largest if there is no other clique including more
     vertices.

     'maximal.cliques' finds all maximal cliques in the input graph. A
     clique in maximal if it cannot be extended to a larger clique. The
     largest cliques are always maximal, but a maximal clique is not
     neccessarily the largest.

     'clique.number' calculates the size of the largest clique(s).

     The current implementation of these functions searches for maximal
     independent vertex sets (see 'independent.vertex.sets') in the
     complementer graph.

_V_a_l_u_e:

     'cliques', 'largest.cliques' and 'clique.number' return a list
     containing numeric vectors of vertex ids. Each list element is a
     clique.

     'clique.number' returns an integer constant.

_A_u_t_h_o_r(_s):

     Tamas Nepusz ntamas@rmki.kfki.hu and Gabor Csardi
     csardi@rmki.kfki.hu for the R interface and the manual page.

_S_e_e _A_l_s_o:

     'independent.vertex.sets'

_E_x_a_m_p_l_e_s:

     # this usually contains cliques of size six
     g <- erdos.renyi.game(100, 0.3)
     clique.number(g)
     cliques(g, min=6)
     largest.cliques(g)

     # To have a bit less maximal cliques, about 100-200 usually
     g <- erdos.renyi.game(100, 0.03)
     maximal.cliques(g)

