---
name: "Graph::TransitiveClosure"
section: "3pm"
platform: "linux"
package: "libgraph-perl"
version: "1:0.9735-1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/Graph::TransitiveClosure"
---

# Graph::TransitiveClosure(3pm)

create and query transitive closure of graph

## NAME

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)
    # 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 on by default so this is a no-op.
    my $tcg = Graph::TransitiveClosure->new($g, path_vertices => 1);
    $tcg->path_vertices($u, $v)
    # see how many paths exist from $u to $v
    my $tcg = Graph::TransitiveClosure->new($g, path_count => 1);
    $tcg->path_length($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.