cycle_basis

Scilab function
Last update : September 1996

cycle_basis - basis of cycle of a simple undirected graph

### Calling Sequence

  `spc = cycle_basis(g)`

### Parameters

- `g`: graph list
- `spc`: sparse matrix

### Description

First a spanning tree is found by using `min_weight_tree` and then used to find all fundamental cycles with respect to this tree. They are returned as a set of cycles, each cycle being represented by a set of edges. These cycles are returned in a sparse matrix `spc`: each line of this matrix corresponds to a cycle.

The graph `g` is supposed to be a simple undirected and connected graph (`cycle_basis` does not check that the graph is simple, use `graph_simp` before calling it if necessary).

### Examples

    ta=[1 1 2 2 2 3 4 5 5 7 8 8 9 10 10 10 10 10 11 12 13 13 13 14 15 16 16 17 17];
    he=[2 10 3 5 7 4 2 4 6 8 6 9 7 7 11 13 13 15 12 13 9 10 14 11 16 1 17 14 15];
    gt=make_graph('foo',1,17,ta,he);
    gt('node_x')=[283 163 63 57 164 164 273 271 339 384 504 513 439 623 631 757 642];
    gt('node_y')=[59 133 223 318 227 319 221 324 432 141 209 319 428 443 187 151 301];
    gt('edge_color')=modulo([1:(edge_number(gt))],15)+1;
    gt('node_diam')=[1:(gt('node_number'))]+20;
    show_graph(gt);
    g=graph_simp(gt);
    g('edge_color')=modulo([1:(edge_number(g))],15)+1;
    g('node_diam')=gt('node_diam');
    g('default_edge_hi_width')=12;
    show_graph(g);
    spc=cycle_basis(g);
    for kk=1:(size(spc,1)),
      aaa=spc(kk,:);aaa=full(aaa);aaa(aaa==0)=[];
      show_arcs(aaa);
    end;

### See Also

`min_weight_tree`, `graph_simp`,