The main raison d'etre of a linked list is that in compiled languages (but not in Perl) arrays are not supported by element deletion or insertion. But I said 'main' rather than 'only'. It is perfectly reasonable that a class might call for a peer to peer relationship and that just happens to be identical in implementation to a linked list. So without further ado, and covering my eyes to anything too complex that has been suggested (sorry no time before Christmas!) that becomes my recommendation, to whit, create a SIMPLE object solution something like:

package P2Pr;
sub new {
    shift();
    my $ref = bless {};
    $ref -> link( @_ ) if ( @_ ); # support one-stop calls
    return $ref;
}
sub link {
    my ( $obj, $relation, $other ) = @_;
    $obj -> { $relation } = $other;
}

# ... 
1;

# common or garden example ...

use P2Pr;
my $carriage1 = P2Pr -> new();
my $train = P2Pr -> new( 'afore', $carriage1 );
$carriage1 -> link ( 'abaft', $train );
my $carriage2 = new( 'abaft', $carriage1 );
$carriage1 -> link( 'afore', $carriage2 );
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Perl should automatically delete objects that have been unlinked from the list, although I am in the habit of making sure by applying a "delete" + object reference before bypassing a node into oblivion (in the example that could be done just by linking both neighbours of the victim node to each other).