My head is killing me. I'm attempting to convert a HoH containing linkages between items into an AoA containing sets of linked items. Basically, take the following: 
$start = {
           'lineitem' => {
                           'invoice' => 1
                         },
           'market_x_branch' => {
                                  'insurer' => 1
                                },
           'invoice' => {
                          'lineitem' => 1
                        },
           'insurer' => {
                          'market_x_branch' => 1
                        }
};

[download]
and convert it into: 
$end = [
          [
            'lineitem',
            'invoice'
          ],
          [
            'market_x_branch',
            'insurer'
          ]
        ];

[download]

Now, I've got code that will pass that test. That code is: 

foreach my $x (keys %$start)
{
    next unless exists $start->{$x};

    my @values = ($x, keys %{$start->{$x}});
    push @$end, \@values;
    delete $start->{$_} for @values;
}

[download]

The problem is that the following test is failing and I simply cannot wrap my head around it. 

$start = {
          'lineitem' => {
                          'invoice' => 1
                        },
          'invoice' => {
                         'lineitem' => 1,
                         'claim' => 1
                       },
          'insurer' => {
                         'claim' => 1
                       },
          'claim' => {
                       'invoice' => 1,
                       'insurer' => 1
                     }
        };

$end = [
    [
        'invoice',
        'claim',
        'insurer',
        'lineitem',
     ],
];

[download]

The order of the elements in $end and the sub-arrays in $end is completely unimportant, as I'm treating it as a set, not a list.

Any suggestions at all would be greatly appreciated.

Update: Added the code I'm using.

------
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In reply to Reducing HoH to AoA by dragonchild

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