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
    g=load_graph(SCI+'/demos/metanet/mesh1000');
    g('directed')=0;
    ta=g('tail');he=g('head');n=node_number(g);
    show_graph(g,'new',[3000,1000]);
    [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');

### See Also

`perfect_match`