take a look at the Graph module:

use warnings;
use strict;
use Data::Dumper;
use Graph;

my $g = Graph->new(directed => 1);
$g->add_vertex("Contig$_") for (1..11);

while (my $line = <DATA>){
    my @nodes = split( /\s+/,$line );
    $g->add_edge( @nodes );
}
print Dumper $g->weakly_connected_components;

__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
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