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.\" ========================================================================
.\"
.IX Title "Graph::TransitiveClosure 3pm"
.TH Graph::TransitiveClosure 3pm "2009-01-17" "perl v5.10.0" "User Contributed Perl Documentation"
.\" For nroff, turn off justification.  Always turn off hyphenation; it makes
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Graph::TransitiveClosure \- create and query transitive closure of graph
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 2
\&    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 => \*(Aqlength\*(Aq);
\&    $tcg\->path_length($u, $v)
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
You can use \f(CW\*(C`Graph::TransitiveClosure\*(C'\fR to compute the transitive
closure graph of a graph and optionally also the minimum paths
(lengths and vertices) between vertices, and after that query the
transitiveness between vertices by using the \f(CW\*(C`is_reachable()\*(C'\fR and
\&\f(CW\*(C`is_transitive()\*(C'\fR methods, and the paths by using the
\&\f(CW\*(C`path_length()\*(C'\fR and \f(CW\*(C`path_vertices()\*(C'\fR methods.
.PP
For further documentation, see the Graph::TransitiveClosure::Matrix.
.SS "Class Methods"
.IX Subsection "Class Methods"
.ie n .IP "new($g, %opt)" 4
.el .IP "new($g, \f(CW%opt\fR)" 4
.IX Item "new($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.
.SS "Object Methods"
.IX Subsection "Object Methods"
These are only the methods 'native' to the class: see
Graph::TransitiveClosure::Matrix for more.
.IP "is_transitive($g)" 4
.IX Item "is_transitive($g)"
Return true if the Graph \f(CW$g\fR is transitive.
.IP "transitive_closure_matrix" 4
.IX Item "transitive_closure_matrix"
Return the transitive closure matrix of the transitive closure object.
.SS "\s-1INTERNALS\s0"
.IX Subsection "INTERNALS"
The transitive closure matrix is stored as an attribute of the graph
called \f(CW\*(C`_tcm\*(C'\fR, and any methods not found in the graph class are searched
in the transitive closure matrix class.