Graph::TransitiveClosure  create and query transitive closure of graph
SYNOPSIS
use Graph::TransitiveClosure;
use Graph::Directed; # or Undirected
my $g = Graph::Directed>new;
$g>add_...(); # build $g
# Compute the transitive closure graph.
my $tcg = Graph::TransitiveClosure>new($g);
$tcg>is_reachable($u, $v) # Identical to $tcg>has_edge($u, $v)
# Being reflexive is the default, meaning that null transitions
# (transitions from a vertex to the same vertex) are included.
my $tcg = Graph::TransitiveClosure>new($g, reflexive => 1);
my $tcg = Graph::TransitiveClosure>new($g, reflexive => 0);
# is_reachable(u, v) is always reflexive.
$tcg>is_reachable($u, $v)
# The reflexivity of is_transitive(u, v) depends of the reflexivity
# of the transitive closure.
$tcg>is_transitive($u, $v)
# You can check any graph for transitivity.
$g>is_transitive()
my $tcg = Graph::TransitiveClosure>new($g, path_length => 1);
$tcg>path_length($u, $v)
# path_vertices is automatically always on so this is a noop.
my $tcg = Graph::TransitiveClosure>new($g, path_vertices => 1);
$tcg>path_vertices($u, $v)
# Both path_length and path_vertices.
my $tcg = Graph::TransitiveClosure>new($g, path => 1);
$tcg>path_vertices($u, $v)
$tcg>length($u, $v)
my $tcg = Graph::TransitiveClosure>new($g, attribute_name => 'length');
$tcg>path_length($u, $v)
DESCRIPTION
You can use Graph::TransitiveClosure
to compute the transitive closure graph of a graph and optionally also the minimum paths (lengths and vertices) between vertices, and after that query the transitiveness between vertices by using the is_reachable()
and is_transitive()
methods, and the paths by using the path_length()
and path_vertices()
methods.
For further documentation, see the Graph::TransitiveClosure::Matrix.
Class Methods
 new($g, %opt)

Construct a new transitive closure object. Note that strictly speaking the returned object is not a graph; it is a graph plus other stuff. But you should be able to use it as a graph plus a couple of methods inherited from the Graph::TransitiveClosure::Matrix class.
Object Methods
These are only the methods 'native' to the class: see Graph::TransitiveClosure::Matrix for more.
 is_transitive($g)

Return true if the Graph $g is transitive.
 transitive_closure_matrix

Return the transitive closure matrix of the transitive closure object.
INTERNALS
The transitive closure matrix is stored as an attribute of the graph called _tcm
, and any methods not found in the graph class are searched in the transitive closure matrix class.