while (my ($k,$v) = first %hash)
{
  delete $hash{$_} for $k, @$v;
}
##</code><code>##

use strict;
use warnings;
use feature 'say';
use Data::Dump qw( pp );

sub first (\%)
{
  my $hash = shift;
  scalar(keys %$hash); # Force reset
  each %$hash;
}

my %hash = 
(
  1 => [2..7],
  8 => [ 9 ],
  9 => [ 8 ],
  (map { $_ => [ 1 ] } 2..7),
);

say "Input hash:", pp \%hash;
say "";

say "Try first then each twice in a row to check that the iteration is restarted";
say pp [first %hash], [each %hash] for 1..2;
say "";

# Delete a key and all the keys contained in the value array
sub rec_delete(\%$);
sub rec_delete(\%$) 
{
  my ($hash, $key) = @_;
  my $array = delete $hash->{$key};
  return unless $array;
  say "     Removing $key -> [ @$array ]";
  rec_delete %$hash => $_ for @$array;
}

while (my ($k,$v) = first %hash)
{
  say "Starting from $k -> [ @$v ]";
  rec_delete %hash => $k;
}
##</code><code>##

Input hash:{ 1 => [2 .. 7], 2 => [1], 3 => [1], 4 => [1], 5 => [1], 6 => [1], 7 => [1], 8 => [9], 9 => [8] }

Try first then each twice in a row to check that the iteration is restarted
([8, [9]], [5, [1]])
([8, [9]], [5, [1]])

Starting from 8 -> [ 9 ]
     Removing 8 -> [ 9 ]
     Removing 9 -> [ 8 ]
Starting from 5 -> [ 1 ]
     Removing 5 -> [ 1 ]
     Removing 1 -> [ 2 3 4 5 6 7 ]
     Removing 2 -> [ 1 ]
     Removing 3 -> [ 1 ]
     Removing 4 -> [ 1 ]
     Removing 6 -> [ 1 ]
     Removing 7 -> [ 1 ]
##</code><code>##

While the hash isn't empty
  Take one key (at random) from the hash
    Delete that key and all connected keys