Here's how I solved my problem:

Beginning file:

 open (BEGIN_FILE, "$beg_file") || die  "Cannot open: $!\n"; 
   while ($line = <BEGIN_FILE>) {
     chomp $line;
     next if ($line =~ /unknown|shutdown|NONE/);
     ($as,$as_name,$nbr,$rtr,$int,$address,$int_name,$ifindex,$vpi,$vc
+i) = split(' ',$priv_line);
     $begin{$int_name} = $rtr;
   }
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All the rest of the files:

foreach $file(@end) {
     open FILE, "$file" || die "Cannot open: $!\n";
     while ($line = <FILE>) {
       chomp $line;
      next if ($line =~ /unknown|shutdown|NONE/);
        ($as,$as_name,$nbr,$rtr,$int,$address,$int_name,$ifindex,$vpi,
+$vci) = split(' ',$priv_line);
     $end{$int_name} = $rtr;    
     }
   }
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Then, in order to end up with a hash of arrays, containing files that exist in my "non-beginning" files, but not in the beginning file:

 my  %good_files = ();
   
   foreach  $key (sort keys %end) {
     if (!exists($begin{$key})){
       push (@{$good_files{$begin{$key}}}, ($key));
       
     }
   }
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Works like a charm! Thanks to everyone for their help on this.