In addition to moritz's comment, be aware that the  //x modifier used in your posted code with the  /module (\w+) \{ ($parens) \};?/gx regex means that whitespace is a comment, so you are looking for "the substring 'module', followed immediately by one or more \w characters, followed immediately by a '{' character, etc..."

As moritz said, lexical variables do not play well with the  (??{ code }) Extended Patterns variant; it is really intended to work with package variables. The following works for me (note that  $parens is a fully local-ized package variable):

use warnings;
use strict;


use constant DENT => '  ';

our $parens;

my $text = do { local $/;  <DATA> };

sub parse {

    my ($text, $indent) = @_;

    $indent = 0 unless defined $indent;

    local $parens = qr{ (?: [^{}]+? | \{ (??{$parens}) \} )* }xms;

    while ($text =~ /module \s+ (\w+) \s* \{ ($parens) \} ;? /gx) {
        my ($name, $content) = ($1, $2);
        print DENT x $indent, qq(subgraph $name { \n);
        ++$indent;
        parse($content, $indent);
        print DENT x $indent, qq(} \n);
        --$indent;
        }
    }

# print $text;  # FOR DEBUG

print "digraph G\n{\n";

parse($text);

print "}\n";

__DATA__
module abc
{
    module def
    {
        module ghi
        {  module jkl {}
        };
    };
};
[download]

Output:

digraph G
{
subgraph abc {
  subgraph def {
    subgraph ghi {
      subgraph jkl {
        }
      }
    }
  }
}
[download]

Updates:

1. Run under ActiveState Perl 5.8.2.808.
2. Quoted regex narration for clarity.