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min_weight_tree(1) Scilab function min_weight_tree(1)
NAME
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)
EXAMPLE
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);
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