I don't really know what you mean by "non-reciprocal edges", but if I get it right, then you want want to find all the connected components in a directed graph, so try this:

use strict;
use warnings;
use Data::Dump qw( pp );

sub find_parts {
  my %graph = %{ shift() };

  my %seen;
  my @parts;
  my $i = 0;

  my $helper;
  $helper = sub {
    my $start = shift;
    return if $seen{$start}++;
    push @{ $parts[$i] }, $start;
    $helper->($_) for @{ $graph{$start} };
  };

  for ( keys %graph ) {
    $helper->($_);
    $i = $#parts + 1;
  }
  undef $helper;

  return @parts;
}

my %graph;

while (<DATA>) {
  my ( $src, $dst ) = split;
  push @{ $graph{$src} }, $dst;
}

pp \%graph;
pp find_parts( \%graph );

__DATA__
Contig1  Contig2
Contig1  Contig3
Contig2  Contig1
Contig2  Contig3
Contig3  Contig1
Contig3  Contig2
Contig3  Contig4
Contig4  Contig3
Contig4  Contig5
Contig6  Contig7
Contig7  Contig6
Contig8  Contig9
Contig9  Contig10
Contig10 Contig8
Contig10 Contig11
Contig11 Contig10
foo bar
bar foo
quux quux
[download]

I haven't tested all the edge cases, but this will give you the idea.

Hope that helps.

update: LanX is right, my code above does not work for the case he has shown. Something like this would have been better to implement: Tarjan's strongly connected components algorithm

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