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.TH max_clique 1 "September 1996" "Scilab Group" "Scilab function"
.so ../sci.an
.SH NAME
max_clique - maximum clique of a graph
.SH CALLING SEQUENCE
.nf
[size,nodes] = max_clique(g,[ind])
.fi
.SH PARAMETERS
.TP 2
g
: graph list
.TP 4
ind
: integer (optional)
.TP 5
size
: integer
.TP 6
nodes
: integer row vector
.SH DESCRIPTION
\fVmax_clique\fR computes the maximum clique of the graph \fVg\fR i.e. the
complete subgraph of maximum size. \fVind\fR is a parameter for the choice
of the method: if \fVind\fR is 0 the method is a partial enumerative
algorithm and if \fVind\fR is 1 the algorithm is based on quadratic
zero-one programming. The default is 0.
The output \fVsize\fR is the number of the nodes of the clique found by the
algorithm and \fVnodes\fR is the vector of the corresponding nodes.
.SH EXAMPLE
.nf
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);
.fi
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