Maintain horizontal ordering of nodes in Graphviz - graphviz

Question

I have the following the dot file contents:
digraph G {
start -> {a0, b0} -> end;
start -> c0 -> c1 -> c2 -> end;
start -> d0 -> d1 -> d2 -> end;
start -> {e0, f0} -> end;
subgraph cluster_test {
{
rank = same;
a0; b0; c0; d0; e0; f0;
}
{
rank = same;
c1; d1;
}
{
rank = same;
c2; d2;
}
}
}
The resulting graph is as follows:
What I want is for the ordering of level 0 nodes to be maintained, i.e, I want a0, b0 to come before c0, d0 in the horizontal direction.
How do I achieve this?

Answer 1

Empty nodes, edges with weight and explicit ordering of the top row in the cluster helps. See code below with annotations:
digraph so
{
// we define all nodes in the beginning, before edges and clusters
// may not be essential but I think it's good practice
start
a0 b0 c0 d0 e0 f0
c1 d1
c2 d2
end
// we define "empty" nodes that can be used to route the edges
node[ shape = point, height = 0 ];
ax bx ex fx
subgraph cluster_test
{
// we need to keep explicit order of the top nodes in the cluster
{ rank = same; a0 -> b0 -> c0 -> d0 -> e0 -> f0[ style = invis ] }
// the original layout in the cluster, empty nodes added at the bottom
{ rank = same; c1 d1 }
{ rank = same; ax bx c2 d2 ex fx }
c0 -> c1 -> c2;
d0 -> d1 -> d2;
// routing through invisible nodes keeps the position of all other nodes
// edges with no arrowheads, strong weight to keep it vertical
edge[ dir = none, weight = 10 ]
a0 -> ax;
b0 -> bx;
e0 -> ex;
f0 -> fx;
}
// connecting to the start and end node, normal edges again
edge[ weight = 1, dir = forw ];
start -> { a0 b0 c0 d0 e0 f0 }
{ ax bx c2 d2 ex fx } -> end;
}
which gives you