#!/usr/bin/perl -w
use strict;
use warnings;
use Data::Dumper;
use Algorithm::EquivalenceSets;

my %groupOfBact = (
    group1 => {
        strain1=>1,
        strain2=>1,
        strain4=>1,
    } ,

    group2 => {
        strain3=>1,
        strain4=>1,
        strain5=>1,
    } ,

    group3 => {
        strain6=>1,
        strain7=>1,
    },
);

print Dumper(\%groupOfBact);

my @sets = map { [ keys %{$groupOfBact{$_}} ] } keys %groupOfBact;

print Dumper(\@sets);

my @equiv_sets = equivalence_sets(\@sets);

print Dumper(\@equiv_sets);
[download]

produces

$VAR1 = {
          'group2' => {
                        'strain5' => 1,
                        'strain3' => 1,
                        'strain4' => 1
                      },
          'group1' => {
                        'strain2' => 1,
                        'strain4' => 1,
                        'strain1' => 1
                      },
          'group3' => {
                        'strain7' => 1,
                        'strain6' => 1
                      }
        };
$VAR1 = [
          [
            'strain5',
            'strain3',
            'strain4'
          ],
          [
            'strain2',
            'strain4',
            'strain1'
          ],
          [
            'strain7',
            'strain6'
          ]
        ];
$VAR1 = [
          [
            'strain7',
            'strain6'
          ],
          [
            'strain2',
            'strain4',
            'strain1',
            'strain5',
            'strain3'
          ]
        ];
[download]

#!/usr/bin/perl -w
use strict;
use warnings;
use Data::Dumper;
use Graph;

my %groupOfBact = (
    group1 => {
        strain1=>1,
        strain2=>1,
        strain4=>1,
    } ,

    group2 => {
        strain3=>1,
        strain4=>1,
        strain5=>1,
    } ,

    group3 => {
        strain6=>1,
        strain7=>1,
    },
);

print Dumper(\%groupOfBact);

my $graph = Graph::Undirected->new;

foreach my $group (keys %groupOfBact) {
    foreach my $strain (keys %{$groupOfBact{$group}}) {
        $graph->add_edge($group, $strain);
    }
}

my @cc = $graph->connected_components();

print Dumper(\@cc);
[download]

Which produces

$VAR1 = {
          'group2' => {
                        'strain5' => 1,
                        'strain3' => 1,
                        'strain4' => 1
                      },
          'group1' => {
                        'strain2' => 1,
                        'strain4' => 1,
                        'strain1' => 1
                      },
          'group3' => {
                        'strain7' => 1,
                        'strain6' => 1
                      }
        };
$VAR1 = [
          [
            'strain7',
            'group3',
            'strain6'
          ],
          [
            'strain3',
            'group2',
            'strain5',
            'strain4',
            'group1',
            'strain1',
            'strain2'
          ]
        ];
[download]

The Graph module gives you many options for entering your data and analyzing it.