That makes it more interesting. If you discover any more interesting cases however you'd better tell us what the application actually is and give us the bigger picture.

use strict;
use warnings;

my %pairs;

while (<DATA>) {
    chomp;
    next if ! length;

    my @pair = sort split;
    ++$pairs{$pair[0]}{$pair[1]};
}

for my $first (sort keys %pairs) {
    my @hits;
    my $count = 0;
    my @implied;

    for my $second (keys %{$pairs{$first}}) {
        next if $pairs{$first}{$second} < 2;

        push @implied, $second;
        ++$count;

        if (exists $pairs{$second}{$first}) {
            delete $pairs{$second}{$first};
            ++$count;
        }

        print "$first $second\n";
    }

    next if ! $count;

    @implied = sort @implied;
    if (@implied == 2 && $pairs{$implied[0]}{$implied[1]}) {
        ++$count;
        delete $pairs{$implied[0]}{$implied[1]};
        @implied = ();
    }

    print "$count";
    print " [not present in @implied]" if @implied == 2;
    print "\n\n"
}

__DATA__
AP_01 AP_02
AP_02 AP_01
AP_01 AP_03
AP_03 AP_01
NP_01 NP_02
NP_02 NP_01
NP_01 NP_03
NP_03 NP_01
NP_02 NP_03
NP_03 NP_02
NP_04 NP_05
NP_06 NP_07
NP_07 NP_06
[download]

Prints:

AP_01 AP_02
AP_01 AP_03
2 [not present in AP_02 AP_03]

NP_01 NP_03
NP_01 NP_02
3

NP_06 NP_07
1
[download]

I added the AP_dd set to make it clearer which groups were which and to provide data to demonstrate the third case.