Thank you very much, Corion .

I did think about a loop but it seems that I needed that the pope gives me a kick :-) I must admit however that I could not wrap my head around the flag $changed yet. Could you please give me another hint on this? Below is my new attempt with the do ... while loop. I updated the sample data to see that the longer chain will be proceeded.

!/perl
use strict;
use warnings FATAL => qw(all);

use Text::CSV_XS;
use Data::Dump;

my $csv_par = 
{ 
 binary => 1, auto_diag => 1, allow_whitespace => 1,    
 sep_char => ';', eol => $/, quote_char => undef, 
};

my $csv = Text::CSV_XS->new($csv_par);
my @data = @{ $csv->getline_all(*DATA) };
shift @data; # simply throw away the header.

my %main;
my %hash_old;

############### The first pass:
for my $row ( @data )
{
   $hash_old{$row->[0]} = $row->[1];
   $main{$row->[0]} = $row->[1];
}

my %hash_new;
############### All the remaining steps:
do
{
  
  for my $row (@data)
  {
     if ( $hash_old{$row->[1]} )
     {
        $hash_new{$row->[0]} = $row->[1];
        $main{ $row->[0] } = 
                  $main{ $row->[1] } || $row->[1];
     }
  }
  %hash_old = ();
  $hash_old{$_} = $hash_new{$_} for keys %hash_new;
  %hash_new = ();
}
while ( scalar keys %hash_old );

############### Filling in the main number 
############### for the main number themselves:
for my $row ( @data )
{
  $main{$row->[1]} = $row->[1] 
    unless exists $main{$row->[1]} or $row->[1] eq "";
  $main{$row->[0]} = $row->[0]
    unless length($main{$row->[0]});  
}

# Sample chains:

# 123-234-345-456-567-678-789
# 117-228-339
# 131
# 213-324-435
# 372

dd \%main;
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The output now:

{
  117 => 117,
  123 => 123,
  131 => 131,
  213 => 213,
  228 => 117,
  234 => 123,
  324 => 213,
  339 => 117,
  345 => 123,
  372 => 372,
  435 => 213,
  456 => 123,
  567 => 123,
  678 => 123,
  789 => 123,
}
[download]