graphviz : how to fix the order and alignment of clusters - graphviz

Question

I try to represent a graph called "dynamic Bayesian network". This graph is composed of a sequence of cluster representing different timeslices (from 0 to N). In each timeslice, I would have the same node, in the same order. Edges only are between nodes in the same timeslice or from a timeslice to the next one.
For instance :
However, from time to time, the ordering of the clusters is not correct. Here timeslice 2 is before timeslice 1 ...
Here is the dot file I have for the second one :
digraph G {
rankdir=TD;
splines=ortho;
node [color="#000000", fillcolor=white, style=filled];
subgraph cluster_0 {
bgcolor="#DDDDDD";
label="Time slice 0";
rankdir=TD;
"P0" [label="P"];
"R0" [label="R"];
"dP0" [label="dP"];
"dR0" [label="dR"];
}
subgraph cluster_1 {
bgcolor="#DDDDDD";
label="Time slice 1";
rankdir=TD;
"P1" [label="P"];
"R1" [label="R"];
"dP1" [label="dP"];
"dR1" [label="dR"];
}
subgraph cluster_2 {
bgcolor="#DDDDDD";
label="Time slice 2";
rankdir=TD;
"P2" [label="P"];
"R2" [label="R"];
"dP2" [label="dP"];
"dR2" [label="dR"];
}
edge [color=blue, constraint=False];
"P0" -> "P1";
"P1" -> "dP1";
"P2" -> "dP2";
"R1" -> "R2";
"R1" -> "dP1";
"R0" -> "dP0";
"dR1" -> "R2";
"R2" -> "dR2";
"dR0" -> "R1";
"dP1" -> "P2";
"P0" -> "dP0";
"P1" -> "P2";
"R2" -> "dP2";
"R0" -> "dR0";
"dP0" -> "P1";
"R0" -> "R1";
"P0" -> "dR0";
"P1" -> "dR1";
"P2" -> "dR2";
"R1" -> "dR1";
edge [constraint=True, style=invis];
"P0" -> "R0";
"R0" -> "dP0";
"dP0" -> "dR0";
"P1" -> "R1";
"R1" -> "dP1";
"dP1" -> "dR1";
"P2" -> "R2";
"R2" -> "dP2";
"dP2" -> "dR2";
}
If I try just to add constraints such as "P0->P1;P1->P2", the order is correct but the clusters are not aligned any more ...
Does someone know how to fix the ordering between the clusters in this graph ?

Answer 1

Changed rankdir direction to guarantee correct sequence of clusters. That in-turn forced rank=same within each cluster, plus a few other tweaks.
digraph G {
rankdir=LR // was rankdir=TD;
splines=ortho;
node [color="#000000", fillcolor=white, style=filled];
subgraph cluster_0 {
bgcolor="#DDDDDD";
label="Time slice 0";
// only applies to Root graph: rankdir=TD;
{rank=same // because we changed rankdir
"P0" [label="P"];
"R0" [label="R"];
"dP0" [label="dP"];
"dR0" [label="dR"];
}
}
subgraph cluster_1 {
bgcolor="#DDDDDD";
label="Time slice 1";
{rank=same
"P1" [label="P"];
"R1" [label="R"];
"dP1" [label="dP"];
"dR1" [label="dR"];
}
}
subgraph cluster_2 {
bgcolor="#DDDDDD";
label="Time slice 2";
{rank=same
"P2" [label="P"];
"R2" [label="R"];
"dP2" [label="dP"];
"dR2" [label="dR"];
}
}
edge [color=blue, constraint=False];
"P0" -> "P1";
"P1" -> "dP1";
"P2" -> "dP2";
"R1" -> "R2";
"R1" -> "dP1";
"R0" -> "dP0";
"dR1" -> "R2";
"R2" -> "dR2";
"dR0" -> "R1";
"dP1" -> "P2";
"P0" -> "dP0";
"P1" -> "P2";
"R2" -> "dP2";
"R0" -> "dR0";
"dP0" -> "P1";
"R0" -> "R1";
"P0" -> "dR0";
"P1" -> "dR1";
"P2" -> "dR2";
"R1" -> "dR1";
// establish positions
edge [style=invis constraint=true]
P0 -> P1 -> P2
R0 -> R1 -> R2
dP0 -> dP1 -> dP2
dR0 -> dR1 -> dR2
}
Giving: