while ( my $input_text = <INP> ) { ....

##</code><code>##

while ( my $line = <INP> ) { 
    chomp $input;
    my ( $cmd, $fnum, $snum ) = split ' ', $line;
    if ( $cmd eq 'q' ) {
        $answered++
            if contains_pair( $connectionText, $fnum, $snum )
            or contains_pair( $connectionText, $snum, $fnum );
        $queries++;
    }
    ...

##</code><code>##

# instead of ... 
        else
        {
            $connectionText.=$fnum.",".$snum."|";
        }
        $connectionText=~s/,,/,/g;
        $connectionText=~s/,\|/\|/g;
# how about ... 
        else
        {
            my $pair = join ',', grep { defined } ( $fnum, $snum );
            $connectiontext .= $pair . '|';
        }

##</code><code>##

push @allPairs, grep { defined } ( $fnum, $snum );

# and at another time .. 

# find half-pairs, which I think is impossible

my @halves = grep { scalar @$_ == 1 && ( $_->[0] == $fnum || $_->[0] == $snum ) } @allpairs;

# find true pairs with a leading fnum

my @matches = grep ( scalar @$_ == 2 && $_->[0] == $fnum } @allpairs

# or a trailing fnum

my @matches = grep ( scalar @$_ == 2 && $_->[1] == $fnum } @allpairs