Thanks for fun, dragonchild!

#!/usr/bin/perl -w 

use strict;

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


my %seen_set;
my $end = [];


foreach my $k (keys %$start) {
    next if exists $seen_set{$k};
    my %set;
    recur(\%set, $k);
    next unless keys %set;
    push @$end, [keys %set];
    @seen_set{keys %set} = ();    
}

sub recur {
    my ($set, $k) = @_;
    return if exists $seen_set{$k} or exists $set->{$k};
    $set->{$k} = 1;
    recur($set, $_) foreach keys %{$start->{$k}};
}

use Data::Dumper;
print Dumper($end);
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