A plain old hash is an unordered container. Sorting the keys does not sort the container, it just gives you a sorted list of keys to work with. The underlying container is unaffected by your sort operation. The order you are seeing when you dump the structure is unreliable and should not be thought of as ordered.

If you need output to be in a specific order you probably need to sort on output. I assume your goal is not to get Data::Dumper to output in a sorted order, but it does serve as a good example: By setting $Data::Dumper::Sortkeys = sub { ... }, you can control the sort order of the data being dumped. The trick will be to compose a subroutine that detects which levels should be sorted, and which should not, and that applies the sort algorithm that you've used in your example code only when appropriate.

So that's how it could be done with Data::Dumper. Your specific use case will be different, but the idea is similar; rather than relying on the hash to be in a particular order, assure that you deal with its elements in the order you prefer.

I'm using Data::Dumper just to display the hash. To solve my problem, I'm storing the keys in the inner hash within an array but the value gets dropped. So I'll assume I'll have to store the value with the key.

my %sorted;

for my $key (keys %bigrams) {
    my $hash = $bigrams{$key};
    for my $secKey (sort { $hash->{$a}<=>$hash->{$b} } keys %$hash) {
        my $value = $hash->{$secKey} / $freqs{$key};
        push( @{ $sorted{$key} }, [$secKey,$value] );
    }
}

while ( my ( $key, $aoa ) = each %sorted ) {
    print "$key\n";
    for my $ary ( @$aoa ) {
        print "\t$ary->[0] => $ary->[1]\n";
    }
}
[download]

like
    VBP => 0.0882352941176471
    VB => 0.0882352941176471
    IN => 0.823529411764706
kind
    JJ => 0.2
    NN => 0.8
capped
    VBN => 0.333333333333333
    JJ => 0.666666666666667
successful
    JJ => 1
distribution
    NN => 1
[download]

Hashes are unsorted by definition. The most common case is that you just want them sorted on output, in which case see for example How do I sort a hash (optionally by value instead of key)?, as well as Data::Dumper's Sortkeys option. If you really, really need to store them in a sorted order, see How can I always keep my hash sorted? (although sometimes people will solve this by simply keeping an array with the names of the keys in a sorted order, and use that to iterate over the hash)

I don't need to display the hash at all. Later on in the program I am storing just the key within an array,

@tags = keys %{ $bigrams{$element}}
[download]

Is there a way to sort the key by there value.

Yes! here is a short program to illustrate the idea:

#/usr/bin/perl
use warnings;
use strict;

my %hash = (a => 4,
            b => 6,
            c => 2);
            
my @sorted_keys = sort keys %hash;
print "@sorted_keys\n";

my @sort_by_value = sort{my $A = $hash{$a};
                         my $B = $hash{$b};
                            $A <=> $B  ## or cmp for strings
                        }keys %hash;
                        
print "@sort_by_value\n";

__END__
Prints:
a b c  # simple key sort
c a b  # keys sorted by value of keys
[download]

The sort{} takes input from the right and sends the same output to the left except in a different order. What goes inside the {} are the "rules" for how to sort the input. $a and $b are special Perl variables that are assigned various values as needed to sort the input. The "return value" of the sort {} should be <0,0,>0 just like the cmp statement does for strings or the "spaceship" operator, <=> does for numbers.