our @preorder_memoized;
sub preorder_tree_walk{
	my ($G, $root, $output) = @_;
	 print "$root \n";
	 print {$output} "$root \n";
	 my @edge_vertices;
	 my $edge_numb = my @e = $G->edges_from($root);
	 if($edge_numb < 1){return;}
	 
	 push(@preorder_memoized, $root);
	 push(@edge_vertices, $_->[1]) foreach @e;
	 
	 #build the tree structure as it would be represented in Euclidean space. 
	 my @sorted_vertices = sort {$G->get_vertex_attribute($a,"X") <=> $G->get_vertex_attribute($b,"X") or
						         $G->get_vertex_attribute($a,"Y") <=> $G->get_vertex_attribute($b, "Y") } @edge_vertices;
	 #print "sorted_ = @sorted_vertices \n";
	 foreach my $edge (@sorted_vertices){
		 if($edge ~~ @preorder_memoized){next;}
		 preorder_tree_walk($G, $edge, $output);		 
		 }
}