Your method does not work for $tolerance > 1 - at least not how I understand the question :)

My solution is based on the OP's statement

So in principle every element in the array will be a centroid (except the first one, in this case it is 0).

use warnings;
use strict;
    
my @nlist = (0,1,2,3,4,5,6,8,10);
my @key_list = ('A'..'Z');
my $tolerance = 2;
my %hoa;

for my $i (1..$#nlist) {
    my $key = shift @key_list;
    $hoa{$key} = [grep in_range($nlist[$i], $_), @nlist ];
}

print "$_ => [@{$hoa{$_}}]\n" for sort keys %hoa;

sub in_range
{
    my ($centroid, $testnum) = @_;
    return abs($centroid - $testnum) <= $tolerance;
}
[download]

which outputs (with tolerance 2):

A => [0 1 2 3]
B => [0 1 2 3 4]
C => [1 2 3 4 5]
D => [2 3 4 5 6]
E => [3 4 5 6]
F => [4 5 6 8]
G => [6 8 10]
H => [8 10]
[download]