Graph::TransitiveClosure(3pm)				User Contributed Perl Documentation			     Graph::TransitiveClosure(3pm)

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 no-op.
	   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.

perl v5.10.0							    2009-01-17					     Graph::TransitiveClosure(3pm)