What you've got sounds like a directed graph, and CPAN has the module Graph. I'm also using Text::CSV to make parsing and output more robust (also install Text::CSV_XS for speed).

input.csv:

personA,personB,10
personB,personA,190
personA,personC,23
personA,personD,43
personE,personF,10
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Code:

#!/usr/bin/env perl
use warnings;
use strict;
use Text::CSV;
use Graph;

my $filename = 'input.csv';

my $g = Graph->new(directed=>1);

open my $fh, '<', $filename or die "$filename: $!";
my $csv = Text::CSV->new({ binary=>1, auto_diag=>2, eol=>$/ });
while ( my $row = $csv->getline($fh) ) {
    my ($author1, $author2, $interactions) = @$row;
    $g->set_edge_attribute( $author1, $author2, # auto-creates edge
        'interactions', $interactions );
}
$csv->eof or $csv->error_diag;
close $fh;

for my $e ($g->edges) {
    my ($author1, $author2) = @$e;
    next if $g->has_edge($author2, $author1);
    my $interactions = $g->get_edge_attribute( $author1, $author2,
        'interactions' );
    $csv->print(select, [ $author1, $author2, $interactions ]);
}
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Output:

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

Update: The above does not handle the case of duplicates in the input. Is that a concern for you, and if yes, what happens with the "interactions"? Are they supposed to be summed up?