Graphviz: forbid horizontal edges, always show vertical orientation - graphviz

Question

I have a directed acyclic graph that I am trying to visualize using Graphviz's dot. By default it's laid out top-to-bottom.
Usually, all directed edges have their head lower than their tail. But in certain cases they're drawn as a horizontal straight line section, i.e. head and tail are at the same level. In my case this happened after I defined subgraph clusters.
Is their a way to forbid this and force it to always position nodes so that the arrows are pointing "downwards"?
Sample source:
digraph {
rankdir=TB;
subgraph cluster_1 { "8"; "7"; "9"; "11"; "10" }
subgraph cluster_2 { "3"; "4"; "5"; }
"1" -> "3";
"2" -> "5";
"3" -> "6";
"3" -> "5";
"2" -> "8";
"2" -> "4";
"2" -> "3";
"2" -> "6";
"2" -> "7";
"1" -> "8";
"7" -> "8";
"4" -> "6";
"6" -> "10";
"3" -> "11";
"7" -> "10";
"7" -> "6";
"1" -> "2";
"6" -> "5";
"7" -> "9";
"7" -> "5";
"4" -> "5";
"6" -> "8";
"3" -> "4";
"10" -> "11";
"4" -> "11";
"3" -> "8";
"8" -> "9";
"6" -> "9";
"9" -> "10";
"3" -> "10";
"3" -> "7";
}

Answer 1

I know this is an old question, but I will provide this answer for future reference:
You could use newrank = true; which does the following according to the graphviz.org website:
The original ranking algorithm in dot is recursive on clusters. This can produce fewer ranks and a more compact layout, but sometimes at the cost of a head node being place on a higher rank than the tail node. It also assumes that a node is not constrained in separate, incompatible subgraphs. For example, a node cannot be in a cluster and also be constrained by rank=same with a node not in the cluster.
If newrank=true, the ranking algorithm does a single global ranking, ignoring clusters. This allows nodes to be subject to multiple constraints. Rank constraints will usually take precedence over edge constraints.
So your source only changes as follows:
digraph {
rankdir=TB;
newrank = true;
...
And the result will be much nicer for this example:

Answer 2

That behaviour is caused by the clusters which fix the node rank inside. 'Force' from outside edges does pull nodes horizontally but has no influence on the rank.
You have to either avoid clusters or insert invisible nodes and edges.
A minimal example showing the rank fix
digraph {
subgraph cluster_1 {
1
3
}
1 -> 2
2 -> 3
}