First of all your die is not very informative. That should be fixed.

Secondly what you need to do is walk through the file building up a data structure with your info, then walk through that and print. Something like this (untested) code:

open (PRV, "<$private") or die "Cannot read $private: $!";
my %connected;
while (<PRV>) {
    chomp;
    my ($far, $dev) = (split(' ', lc($_)))[0,3];
    push @{$connected{$far}}, $dev;
}

foreach my $dev (sort keys %connected) {
  my $fars = join ", ", @{$connected{$dev}};
  print "$dev is connected to: $fars\n";
}
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