my @input = qw(0:6
0:12
0:18
0:24
6:12
6:18
6:24
12:18
12:24
18:24);

my %link;
for (@input) {
    my ($key, $value) = split /:/;
    push @{$link{$key}}, $value;
}
[download]

$VAR1 = {
          '6' => [
                   '12',
                   '18',
                   '24'
                 ],
          '18' => [
                    '24'
                  ],
          '0' => [
                   '6',
                   '12',
                   '18',
                   '24'
                 ],
          '12' => [
                    '18',
                    '24'
                  ]
        };
[download]

You then just need to connect the dots, which I'd probably implement with a recursive subroutine.

Note that the confusion about the start and end definition of your chains likely comes from the fact that, in your example, you seem to use all possible values for starts, but only 24 as an end.