Scilab function

best_match - best matching of a graph

### Calling Sequence

[card,match] = best_match(g)

### Parameters

• g : graph list
• card : integer
• match : integer row vector

### Description

best_match finds an optimal matching for the graph g. The output are card and the vector match. card is the cardinality of an optimal matching. match(i) is the node adjacent to node i in the optimal matching or 0 if i is unmatched.

### Examples

```ta=[27 27 3 12 11 12 27 26 26 25 25 24 23 23 21 22 21 20 19 18 18];
ta=[ta  16 15 15 14 12 9 10 6 9 17 8 17 10 20 11 23 23 12 18 28];
he=[ 1  2 2  4  5 11 13  1 25 22 24 22 22 19 13 13 14 16 16  9 16];
he=[he  10 10 11 12  2 6  5 5 7  8 7  9  6 11  4 18 13  3 28 17];
n=28;
g=make_graph('foo',0,n,ta,he);
xx=[46 120 207 286 366 453 543 544 473 387 300 206 136 250 346 408];
g('node_x')=[xx 527 443 306 326 196 139 264  55  58  46 118 513];
yy=[36  34  37  40  38  40  35 102 102  98  93  96 167 172 101 179];
g('node_y')=[yy 198 252 183 148 172 256 259 258 167 109 104 253];
show_graph(g);
[card,match] = best_match(g);
sp=sparse([ta' he'],[1:size(ta,2)]',[n,n]);
sp1=sparse([[1:n]' match'],ones(1,size(match,2))',[n,n]);
[ij,v,mn]=spget(sp.*sp1);
show_arcs(v');
//
// WITH A LARGER GRAPH