min_weight_tree

Scilab function
Last update : September 1995

min_weight_tree - minimum weight spanning tree

### Calling Sequence

  `t = min_weight_tree([i],g)`

### Parameters

- `i`: integer, node number of the root of the tree
- `g`: graph list
- `t`: row vector of integer numbers of the arcs of the tree if it exists

### Description

`min_weight_tree` tries to find a minimum weight spanning tree for the graph `g`. The optional argument `i` is the number of the root node of the tree; its default value is node number 1. This node is meaningless for an undirected graph.

The weights are given by the element `edge_weight` of the graph list. If its value is not given (empty vector `[]`), it is assumed to be equal to 0 on each edge. Weigths can be positive, equal to 0 or negative. To compute a spanning tree without dealing with weights, give to weights a value of 0 on each edge or the empty vector `[]`.

`min_weight_tree` returns the tree `t` as a row vector of the arc numbers (directed graph) or edge numbers (undirected graph) if it exists or the empty vector `[]` otherwise. If the tree exists, the dimension of `t` is the number of nodes less 1. If `t(i)` is the root of the tree: - for j < i, `t(j)` is the number of the arc in the tree after node `t(j)` - for j > i, `t(j)` is the number of the arc in the tree before node `t(j)`

### Examples

    ta=[1 1 2 2 2 3 4 5 5 7 8 8 9 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 15 12 13 9 10 14 11 16 1 17 14 15];
    g=make_graph('foo',1,17,ta,he);
    g('node_x')=[283 163 63 57 164 164 273 271 339 384 504 513 439 623 631 757 642];
    g('node_y')=[59 133 223 318 227 319 221 324 432 141 209 319 428 443 187 151 301];
    show_graph(g);
    t=min_weight_tree(1,g);
    g1=g; ma=arc_number(g1); n=g1('node_number');
    nodetype=0*ones(1,n); nodetype(1)=2; g1('node_type')=nodetype;
    edgecolor=1*ones(1,ma); edgecolor(t)=11*ones(t); g1('edge_color')=edgecolor;
    edgewidth=1*ones(1,ma); edgewidth(t)=4*ones(t); g1('edge_width')=edgewidth;
    x_message('Minimum weight tree from node 1');
    show_graph(g1);