NAME

Graph::Weighted - A weighted graph implementation

VERSION

version 0.9

SYNOPSIS

 use Graph::Weighted;

 my $gw = Graph::Weighted->new;
 $gw->populate(
    [ [ 0,1,2,0,0 ], # Vertex 0 with 2 edges of weight 3
      [ 1,0,3,0,0 ], #    "   1      2 "               4
      [ 2,3,0,0,0 ], #    "   2      2 "               5
      [ 0,0,1,0,0 ], #    "   3      1 "               1
      [ 0,0,0,0,0 ], #    "   4      0 "               0
    ]
 );
 $gw->dump();

 my ( $lightest, $heaviest ) = $gw->vertex_span;
 ( $lightest, $heaviest ) = $gw->edge_span;

 my $weight = $gw->path_cost( \@vertices );

 my $attr = 'probability';
 $gw = Graph::Weighted->new;
 $gw->populate(
    {
        0 => { label => 'A', 1=>0.4, 3=>0.6 },
        1 => { label => 'B', 0=>0.3, 2=>0.7 },
        2 => { label => 'C', 0=>0.5, 2=>0.5 },
        3 => { label => 'D', 0=>0.2, 1=>0.8 },
    },
    $attr
 );
 $gw->dump($attr);

DESCRIPTION

A Graph::Weighted object is a subclass of the Graph module with attribute handling. As such, all of the Graph methods may be used, with the addition of custom weighting.

METHODS

new()

  my $gw = Graph::Weighted->new;

Return a new Graph::Weighted object.

Please see "Constructors" in Graph for the possible constructor arguments.

populate()

  $gw->populate($matrix);
  $gw->populate($matrix, $attribute);
  $gw->populate(\@vectors);
  $gw->populate(\@vectors, $attribute);
  $gw->populate(\%data_points);
  $gw->populate(\%data_points, $attribute);

Populate a graph with weighted nodes.

The data can be an arrayref of numeric vectors, a Math::Matrix object, a Math::MatrixReal object, or a hashref of edge values.

Data given as a hash reference may also contain multiple node labels. Also, the keys need not be numeric, just unique.

The optional attribute argument is a string with the default "weight."

get_cost()

  $c = $gw->get_cost($vertex);
  $c = $gw->get_cost($vertex, $attribute);
  $c = $gw->get_cost(\@edge);
  $c = $gw->get_cost(\@edge, $attribute);

Return the named attribute value for the vertex or edge. If no attribute name is given, the string "weight" is used.

vertex_span()

 ($lightest, $heaviest) = $gw->vertex_span();
 ($lightest, $heaviest) = $gw->vertex_span($attr);

Return the lightest and heaviest vertices as array references.

edge_span()

 ($lightest, $heaviest) = $gw->edge_span();
 ($lightest, $heaviest) = $gw->edge_span($attr);

Return the lightest and heaviest edges as array references.

path_cost()

 $c = $gw->path_cost(\@vertices);
 $c = $gw->path_cost(\@vertices, $attr);

Return the summed weight (or cost attribute) of the path edges.

For the cost of the shortest path, please see path_length under "All-Pairs Shortest Paths (APSP)" in Graph.

dump()

  $gw->dump()
  $gw->dump($attr)

Print out the graph showing vertices, edges and costs.

EXAMPLES

Shortest Paths

  my $g = Graph::Weighted->new();
  $g->populate({
    A => { B => 4, C => 2 },
    B => { C => 5, D => 10 },
    C => { E => 3 },
    D => { F => 11 },
    E => { D => 4 },
    F => { },
  });
  my @path = $g->SP_Dijkstra( 'A', 'F' ); # A->C->E->D->F
  print 'Dijkstra: ', join( '->', @path ), "\n";

  $g = Graph::Weighted->new();
  $g->populate({
    S => { A =>  7, B => 6 },
    A => { C => -3, T => 9 },
    B => { A =>  8, C => 5, T => -4 },
    C => { B => -5 },
    T => { },
  });
  @path = $g->SP_Bellman_Ford( 'S', 'T' ); # S->A->C->B->T
  print 'Bellman-Ford: ', join( '->', @path ), "\n";

  $g = Graph::Weighted->new();
  $g->populate({
    1 => { 2 => 8, 4 => 1 },
    2 => { 3 => 1 },
    3 => { 1 => 4 },
    4 => { 2 => 2, 3 => 9 },
  });
  my $apsp = $g->APSP_Floyd_Warshall();
  @path = $apsp->path_vertices( 1, 3 ); # 1->4->2->3
  print 'Floyd-Warshall: ', join( '->', @path ), "\n";

Minimum Spanning Trees

  my $g = Graph::Weighted->new( undirected => 1 );
  $g->populate({
        A => { B => 4, F => 2 },
        B => { C => 6, F => 5 },
        C => { F => 1 },
        D => { },
  });

  my @path = $g->MST_Kruskal; # A=B,A=F,C=F
  print 'Kruskal: ', join( '->', @path ), "\n";

  @path = $g->MST_Prim; # same
  print 'Prim: ', join( '->', @path ), "\n";

SEE ALSO

Graph, the parent of this module

Graph::Easy::Weighted, the sibling

The eg/* and t/* file sources

AUTHOR

Gene Boggs <gene@cpan.org>

COPYRIGHT AND LICENSE

This software is copyright (c) 2015 by Gene Boggs.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.

cpanm Graph::Weighted

perl -MCPAN -e shell
install Graph::Weighted