Hello
I am now beginning to wonder at my own sanity as when I run your original code, replacing your data with the following

A1-4100-YZX-002|A1-4100
A1-4100|A1
A1-4200-ABC-001|A1-4200
A1-4200|A1
A1-4100-YZX-002-01|A1-4100-YZX-002
[download]

I get the following output

A1-4100|A1
A1-4200-ABC-001|A1-4200
A1-4100-YZX-002-01|A1-4100-YZX-002
A1-4100-YZX-002|A1-4100
A1-4200|A1
[download]

Which is very different to what your seeing. The full code I am running is..........

#!/usr/bin/perl

use strict;
use warnings;

my %node;

while (<DATA>) {
    my ( $c, $p ) = split;
    if ( $c eq $p ) {  # these are easy, so finish them first
        print;
        next;
    }

    if ( exists( $node{$c}{child_of} )) {
        warn "$.: bad record: $c is child of both $p and $node{$c}{chi
+ld_of}\n";
        next;
    }
    $node{$c}{child_of} = $p;
    $node{$p}{parent_of}{$c} = undef;
}

# begin the sorted output by looping over values that do not have pare
+nts:

for my $parent ( grep { !exists( $node{$_}{child_of} ) } keys %node ) 
+{
    my $children = $node{$parent}{parent_of};  # ref to hash of child 
+values
    trace_down( $children, \%node );
}

sub trace_down
{
    my ( $kids, $tree ) = @_;
    for my $kid ( keys %$kids ) {
        print "$kid $$tree{$kid}{child_of}\n";
        if ( exists( $$tree{$kid}{parent_of} )) {
            trace_down( $$tree{$kid}{parent_of}, $tree );
        }
    }
}

__DATA__
A1-4100-YZX-002|A1-4100
A1-4100|A1
A1-4200-ABC-001|A1-4200
A1-4200|A1
A1-4100-YZX-002-01|A1-4100-YZX-002
[download]

On the question of multiple "TOPS".... There will only ever be one "TOP" which is A1. The reason for this is that there are around 12 (I can't remember the exact number) "children" of A1 which are A1-4100, A1-4200, A1-4300 etc etc etc. Then you have (for example) "A1-4200-ABC-001". I already tried using "grep -w" (match only whole words) and using "sort" (I worked for a number of years on UNIX and still work with Linux) which I thought may fix things, however, the parent-to-child relationship does not follow strict numbering conventions, i.e. the sequence "A1-4200-ABC-001" may be a child of "A1-405-ABC-001-FF".
The top two tiers of the hierarchy follow a numbering convention (A1, A1-4600 etc) and can be followed quite easily, however, the rest has been built by a person and not by any "logical" numbering system so using partial string matching will not work, unfortunately.

I realize I am taking up a lot of your time with this and I do appreciate your input and patience with my coding inadequacies.
SlackyB