max_clique - maximum clique of a graph

Calling Sequence

[size,nodes] = max_clique(g,[ind])

Parameters

• g : graph list
• ind : integer (optional)
• size : integer
• nodes : integer row vector

Description

max_clique computes the maximum clique of the graph g i.e. the complete subgraph of maximum size. ind is a parameter for the choice of the method: if ind is 0 the method is a partial enumerative algorithm and if ind is 1 the algorithm is based on quadratic zero-one programming. The default is 0. The output size is the number of the nodes of the clique found by the algorithm and nodes is the vector of the corresponding nodes.

Examples

ta=[1 2 3 4 5 6 6 7 8  9 10 16 16 10 11 11 12 12 11 14 15 15 13 7 13 13];
he=[2 3 4 5 6 7 8 8 9 10 16  2  3 11 12 13  1 14 14 15  5  9 12 4 14 15];
g=make_graph('foo',0,16,ta,he);
g('node_x')=[106 199 369 467 470 403 399 347 308 269 184 108 199 268 345 272];
g('node_y')=[341 420 422 321 180 212 286 246 193 244 243 209  59 134  51 348];
g('node_diam')=[1:(g('node_number'))]+20;
show_graph(g);
[ns,no] = max_clique(g);
show_nodes(no);
g1=graph_complement(g);
[ns,no] = max_clique(g1);
show_nodes(no);