NAME

Graph::Weighted - An abstract, weighted graph implementation

SYNOPSIS

use Graph::Weighted;

$g = Graph::Weighted->new(
    [ [ 0, 1, 2, 0, 0 ],   # A vertex with two edges.
      [ 1, 0, 3, 0, 0 ],   # "
      [ 2, 3, 0, 0, 0 ],   # "
      [ 0, 0, 1, 0, 0 ],   # A vertex with one edge.
      [ 0, 0, 0, 0, 0 ] ]  # A vertex with no edges.
);

$g = Graph::Weighted->new(
    data => {
      weight => {
          a => { b => 1, c => 2 },  # A vertex with two edges.
          b => { a => 1, c => 3 },  # "
          c => { a => 2, b => 3 },  # "
          d => { c => 1 },          # A vertex with one edge.
          e => {}                   # A vertex with no edges.
      }
   }
);

$g = Graph::Weighted->new(data => $Math_Matrix_object);

$data = $g->weight_data;

$w = $g->graph_weight;

$w = $g->vertex_weight($v1);
$w = $g->vertex_weight($v1, $w + 1);

$w = $g->edge_weight($v1, $v2);
$w = $g->edge_weight($v1, $v2, $w + 1);

$vertices = $g->heaviest_vertices;
$vertices = $g->lightest_vertices;

$w = $g->max_weight;  # Weight of the $heavies vertices.
$w = $g->min_weight;  # Weight of the $lights vertices.

# Call the weight methods of the inherited Graph module.
$x = $g->MST_Kruskal;
$x = $g->APSP_Floyd_Warshall;
$x = $g->MST_Prim($p);

DESCRIPTION

A Graph::Weighted object represents a subclass of Graph::Directed with weighted attributes that are taken from a two dimensional matrix (as an array or hash reference) of numerical values.

This module can also load the matrix portions of Math::Matrix, Math::MatrixReal, and Math::MatrixBool objects.

Initially, the weights of the vertices are set to the sum of their outgoing edge weights. This is mutable, however, and can be reset to any value desired, after initialization, with the vertex_weight and edge_weight methods.

This module allows you to create a graph with edges that have values defined in a given matrix. You can have as many of these matrices as you like. Each one is referenced by an attribute name. For a weighted graph, this attribute is named "weight". For a capacity graph, this attribute is named "capacity". Each attribute corresponds to one matrix of values.

PUBLIC METHODS

• new %ARGUMENTS

  debug => 0 | 1

  Flag to invoke verbose mode while processing. Defaults to zero.

  zero_edges => 0 | 1

  Flag to add edges between vertices with a weight of zero. Defaults to zero.

  default_attribute => STRING

  The attribute to use by default, if the generic (load, data, and *_attr) methods are called without an attribute as an argument (which should never actually happen, if you are doing thing corrdctly).

  This is set to 'weight', by default, of course.

  data => $HASHREF | $ARRAYREF | $OBJECT

  Two dimensional hash, (NxN) array, or known object reference to use for vertices and weighted edges.

  Math::Matrix, Math::MatrixReal, and Math::MatrixBool objects can also be loaded.

• load_weights $HASHREF | $ARRAYREF | $OBJECT

  Turn the given two dimensional hash, (NxN) array, or known object reference into the vertices and weighted edges of a Graph::Directed object.

  Math::Matrix, Math::MatrixReal, and Math::MatrixBool objects can also be loaded.

• weight_data

  Return a two dimensional hash representing the vertices and all their weighted edges.

• graph_weight

  Get the total weight of the graph, which is the sum of the vertex weights.

• vertex_weight $VERTEX [, $WEIGHT]

  Return the weight of a vertex.

  (The vertices are just the keys of the data, not some glorified object, by the way.)

  If a second argument is provided, the vertex weight is set to that value and is distributed evenly to the vertex's outgoing edges, and the total weight of the graph is adjusted accordingly.

• edge_weight $VERTEX, $SUCCESSOR [, $WEIGHT]

  Return the weight of an edge between the two given vertices.

  If a third argument is provided, the weight it represents is used to replace the weight of the edge between the vertex (first argument) and it's successor (second argument). Finally, the weight of the vertex and the total weight of the graph are adjusted accordingly.

• heaviest_vertices

  Return an array reference of vertices with the most weight.

• lightest_vertices

  Return an array reference of vertices with the least weight.

• max_weight

  Return the weight of the heaviest vertices.

• min_weight

  Return the weight of the lightest vertices.

PRIVATE METHODS

• _debug @STUFF

  Print the contents of the argument array with a newline appended.

API METHODS

These are generic methods that are used for the public methods of Graph::Weighted and Graph::Weighted::Capacity. Primarily, they each accept an extra attribute argument and use the class default attribute, if none is provided.

All the following methods are described in greater detail under the PUBLIC METHODS section, above.

• new %ARGS

  Using a default attribute and an array reference:

  $g = Graph::Weighted::Foo->new(
      default_attribute => 'foo',
      data => $array_ref,
  );

  Using a set of data (which can be either array or hash references), with keys as attributes:

  $g = Graph::Weighted::Bar->new(
      data => {
          foo => $data_1,
          bar => $data_2,
          baz => $data_3,
      },
  );

• load $DATA [, $ATTR]

  This method can accept either a Math::Matrix* object, an array or hash reference for the data.

  If given an array reference, the attribute argument or class default attribute is used.

  If given a hash reference, the keys are used as attributes and the values can be either Math::Matrix* objects, array or hash references.

• data [$ATTR]

  $hash_ref = $g->data($attr);

• graph_attr [$ATTR]

  $x = $g->graph_attr($attr);

• vertex_attr $VERTEX [, $VALUE] [, $ATTR]

  This method requires named parameters.

  $x = $g->vertex_attr(
      vertex => $v,
      value => $val,
      attr => $attr,
  );

• edge_attr $VERTEX, $SUCCESSOR [, $VALUE] [, $ATTR]

  This method requires named parameters.

  $x = $g->edge_attr(
      vertex => $v,
      successor => $s,
      value => $val,
      attr => $attr,
  );

• largest_vertices [$ATTR]

  $array_ref = $g->largest_vertices($attr);

• smallest_vertices [$ATTR]

  $array_ref = $g->smallest_vertices($attr);

• max_attr [$ATTR]

  $x = $g->max_attr($attr);

• min_attr [$ATTR]

  $x = $g->min_attr($attr);

SEE ALSO

Graph::Base

Graph::Weighted::Capacity

TO DO

Make the data method emit an array reference as well as a hash reference.

Handle arbitrary string attribute values.

Handle algebraic expression attribute values (probably via Math::Symbolic). Lisp expressions come to mind also...

AUTHOR

Gene Boggs <gene@cpan.org>

COPYRIGHT AND LICENSE

Copyright 2003 by Gene Boggs

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