your problem is not well defined, but the demonstrated results can be achieved with a recursive function:

use strict;
use warnings;
use Data::Dumper;
$|=1;
 
my $start="B";
my $stop="E";
 
my %graph =(
          'F' => ['B','C','E'],
          'A' => ['B','C'],
          'D' => ['B'],
          'C' => ['A','E','F'],
          'E' => ['C','F'],
          'B' => ['A','E','F']
        );
 
track($start);
 
sub track {
  my @path=@_;
  my $last=$path[-1];
  for my $next (@{$graph{$last}}) {
    next if $next ~~ @path;
    # next if grep {$_ eq $next } @path;
    if ($next eq $stop){
      print join ("->",@path,$stop),"\n";
    } else {  
      track(@path,$next);
    }  
  }
}
[download]

prints

B->A->C->E
B->A->C->F->E
B->E
B->F->C->E
B->F->E
[download]

for large graphs you should consider using a hash instead of passing an array to speed up the test.