Set $Data::Dumper::Purity to 1:

#!/usr/bin/perl

use Data::Dumper;
$Data::Dumper::Purity = 1;

$old = { name => "bob" };
$young = { name => "bob jr" };

$old->{child} = $young;
$young->{parent} = $old;

$string = Data::Dumper->Dump([$old],[qw(old)]);

undef $old;
undef $young;

eval "$string";

$check = Data::Dumper->Dump([$old],[qw(old)]);

if ($string ne $check) {
    print "eek!\n";
}

print "\n---\n$string---\n$check\n";
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Data::Dumper's man page says:

The default output of self-referential structures can be `eval'ed, but the nested references to `$VAR'n will be undefined, since a recursive structure cannot be constructed using one Perl statement. You should set the `Purity' flag to 1 to get additional statements that will correctly fill in these references.

Ciao, Valerio