my $VAR1 = {
          'A' => [0,1,2],  # centroid is 1, with  other elem 0 and 2 (1 +/- 1)
          'B' => [1,2,3],
          'C' => [2,3,4],
          'D' => [3,4,5],
          'E' => [4,5,6],
          'F' => [5,6],    # centroid is 6 but only with one elem 5 (i.e. 6-1)
          'G' => [8],      # next centroid is 8 but no members
          'I' => [10],     # same for centroid 10
        };

  # As the @nlist array grow larger the final hash will also grow larger.

##</code><code>##

use strict;              
use Data::Dumper;        
use Carp;                


# Size of this array  could be much greater than this 
my @nlist = ( 0, 1, 2, 3, 4, 5, 6, 8, 10 );

# And the first element can be greater than 0


# This is a pre-generated key candidate.
# It may not be used up all of them
# In practice I will create a large key list,
# that should be greater than  potential hash to be created
my @key_list = ( 'A' .. 'Z' );

my $tolerance = 1;

my $hoa;

foreach my $nlist (@nlist) {
    my @tmpar = ($nlist[0]);

    my $first_elem = $nlist[0];
    my $klist;

    if ( check_member( \@tmpar, $first_elem, $nlist, $tolerance ) == 1 ) {
        push @tmpar, $nlist;
        $klist = shift @key_list;
        push @{ $hoa->{$klist} }, @tmpar;
    }

}

print Dumper $hoa;

# -- Subroutine ------
sub check_member {

    # To check if a value can be
    # a member of an array
    my ( $alist, $fel, $snum,$tol ) = @_;

    my $centroid = $alist->[0];

    if (   $centroid - $tol == $snum
        or $centroid + $tol == $snum
        or $centroid == $snum
        and $centroid != $fel

        )
    {
        return 1;
    }

    return 0;
}