Find Difficulty in Generating a Subgraph DAG using Graphviz - graphviz

Question

I am using graphviz (version 2.40.1 (20161225.0304)) to convert a program-generated dot file to a png. Basically what I want to visualize by the dot file is a subgraph directed acyclic graph, i.e., subgraph DAG in short, where each node of the DAG is a subgraph. For the visualization, I need to present (1) the structure of the DAG; and (2) the topology of the subgraph of each DAG node.
For example, the following dot file generates the following png, where there are 3 DAG nodes and 2 DAG edges. I use cluster to represent the subgraph of each DAG node. I think it's still readable to human.
digraph plan_v1 {
rankdir=LR
compound=true
subgraph cluster28 {
color=black // not query
shape=box
penwidth=3
label="id: 28\ndag id: 0\ncardinality: 100"
{
rank=min
28.0 [shape=box label="id: 0\nlabel: 0"]
28.1 [shape=box label="id: 1\nlabel: 0"]
}
28.0 -> 28.1 [label="label: 0"]
}
subgraph cluster29 {
color=black // not query
shape=box
penwidth=3
label="id: 29\ndag id: 1\ncardinality: 301"
{
rank=min
29.0 [shape=box label="id: 0\nlabel: 0"]
29.1 [shape=box label="id: 1\nlabel: 0"]
}
{
rank=max
29.2 [shape=box label="id: 2\nlabel: 0"]
}
29.0 -> 29.1 [label="label: 0"]
29.0 -> 29.2 [label="label: 0"]
29.1 -> 29.2 [label="label: 0"]
}
28.1 -> 29.0 [ltail=cluster28 lhead=cluster29 penwidth=1 minlen=2 label="latency: 0\ncost: 0\npath cost: 0\nsub tree cost: 479"]
subgraph cluster15 {
color=black // not query
shape=box
penwidth=3
label="id: 15\ndag id: 2\ncardinality: 376"
{
rank=min
15.0 [shape=box label="id: 0\nlabel: 0"]
15.1 [shape=box label="id: 1\nlabel: 0"]
}
{
rank=max
15.2 [shape=box label="id: 2\nlabel: 0"]
}
15.0 -> 15.1 [label="label: 0"]
15.0 -> 15.2 [label="label: 0"]
15.2 -> 15.1 [label="label: 0"]
}
28.1 -> 15.0 [ltail=cluster28 lhead=cluster15 penwidth=1 minlen=2 label="latency: 0\ncost: 0\npath cost: 0\nsub tree cost: 2319"]
}
The problem is, when the number of vertices of the subgraph increases, graphviz uses large space to represent each DAG node that has a large subgraph. I want to reduce the space for large subgraph by controlling the layout of the subgraph vertices. Basically my strategy is, given a subgraph with n vertices, I give min rank to vertex id 0 and 1, max rank to vertex id n-1 and n-2, and I request the rank of vertex 2*i and 2*i+1 to be the same for 0<i<(n-1)/2. Forget to tell that I am a beginner of graphviz so there could be mistake for the design of the above strategy (but not implementation).
With the above strategy, I found that graphviz may not be able to generate png if the subgraph DAG is too complex. Here is an example: https://gist.github.com/zzxx-husky/50c5ad0cf56254dc0e01d7cb6b8389ad .
For the above gist example, if I directly use graphviz to convert it to png, graphviz throws me a segfault
libpath/shortest.c:324: triangulation failed
libpath/shortest.c:192: source point not in any triangle
Error: in routesplines, Pshortestpath failed
Segmentation fault (core dumped)
I tried to add rankdir=LR at the beginning, that may help convert the dot to png successfully, but graphviz still complains a lot of Warning: XXX -> YYY: head not inside head cluster clusterZZZ and the png is ugly (DAG nodes may overlap with each other).
Finally, I have to comment out all the rank=same in the dot if I want to convert the dot to a nice png successfully. However, those large DAG nodes in the png require a lot of space to present their subgraphs and the large subgraphs look a mess.
At the end, I wonder whether my use of rank=same is not correct and how can I reduce the space for presenting a large subgraph. Thanks in advance.
====== Updates at 20200810 ======
To answer #sroush's question, what I want is that those large subgraphs can use less space to present their topologies compactly. Here is how a subgraph with 7 vertices is presented (the left one below). The subgraph edges are too long and bend weirdly. But I hope less space is used, like the right one below, which is more neat and compact. One may point out that the figure below looks smaller is because I removed all the edge label. I wonder whether it is possible to make the subgraph neat while the subgraph edges still carry their labels.

Answer 1

Three possibilities - if you like any of them I'll post the input files. Coloring the edges would probably help.