While Graph can certainly do this for you, understanding the graph theory involved is a good idea. Basically, here's what you do:

• For each available vertex:
  • Select it ($seen{$vertex} = 1)
  • Push the vertex to the current path (push @path, $vertex)
  • If the number of vertices in the path equals the desired length (@path == $len)
    • Store the path in the master list (push @all_paths, [@path])
  • Else:
    • Set "available vertices" to all unseen adjacent vertices (grep { !$seen{$_} } @{ $adjacent{$vertex} })
    • Repeat from top
  • Remove the latest vertex added to the path (pop @path)
  • Un-select the vertex ($seen{$vertex} = 0)

This is a relatively simple recursive process. The code is basically something like:

my $paths_ref = get_paths(\%adjaceny_matrix, $length);


sub get_paths {
  my ($adj, $len) = @_;
  my @paths;
  _get_paths_helper(\@paths, $adj, $len, [], {}, [keys %$adj]);
  return \@paths;
}


sub _get_paths_helper {
  my ($p, $am, $len, $curr, $seen, $avail) = @_;

  for my $v (@$avail) {
    push @$curr, $v;
    local $seen->{$v} = 1;
    if (@$curr == $len) { push @$p, [@$curr] }
    else {
      _get_paths_helper($p, $am, $len, $curr, $seen, [grep { !$seen->{
+$_} } @{ $am->{$v} }]);
    }
    pop @$curr;
  }
}
[download]

This can be modified to allow you to search for multiple depths without having to call the main function multiple times (which would be terribly inefficient!).

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