#!/usr/bin/perl

# https://perlmonks.org/?node_id=1226286

use strict;
use warnings;

my %keep;

while( <DATA> )
  {
  /(\w+),(\w+),/ or next;
  $keep{$2, $1} and delete $keep{$2, $1} or $keep{$1, $2} = $_;
  }
print sort values %keep;

__DATA__
personA,personB,10
personA,personC,23
personA,personD,43
personB,personA,190
personE,personF,10
[download]

Or, of course, the regex version :)

#!/usr/bin/perl

# https://perlmonks.org/?node_id=1226286

use strict;
use warnings;

local $_ = do { local $/, <DATA> };
1 while s/^(\w+),(\w+),.*\n((?:.*\n)*?)^\2,\1,.*\n/$3/gm;
print;

__DATA__
personA,personB,10
personA,personC,23
personA,personD,43
personB,personA,190
personE,personF,10
[download]