Venn Diagram in Dot - dot

Question

I have been trying to implement a Venn Diagram in Dot. Whilst Venn Diagrams probably aren't that useful in Dot, it's mostly so I can use it as a very basic building block.
I have provided some ways that I have tried to do this:
graph G {
subgraph cluster0 {
color=white;
subgraph cluster0 {
label="1";
color=black;
a;
b;
}
subgraph cluster1 {
label="2";
color=black;
b;
c;
}
}
subgraph cluster1 {
color=white;
subgraph cluster2 {
label="1";
color=black;
d;
}
subgraph cluster3 {
label="1+2";
color=black;
e;
}
subgraph cluster4 {
label="2";
color=black;
f;
}
}
subgraph cluster2 {
color=white;
subgraph cluster5 {
label="1";
color=black;
g;
subgraph cluster6 {
label="2";
color=black;
h;
}
}
subgraph cluster6 {
label="2";
color=black;
i;
}
}
a -- d -- g [penwidth=0];
b -- e -- h [penwidth=0];
c -- f -- i [penwidth=0];
}
Producing:
These all have problems:
The first says b is in 1, but not 2. When it should be in both.
The second looks like it's separate from 1 and 2. And can be hard to show it's both.
The third is almost perfect IMO, it just requires the two 2 sub-graphs to join together.
To prevent an XY problem, I have:
two servers,
a docker swarm between the two servers, and
three applications. Located at:
One is on the first server, not in the docker swarm.
One is on the first server in the docker swarm.
One is on the second server in the docker swarm.
Leading to:
graph G {
subgraph cluster0 {
color=white;
subgraph cluster0 {
label="Server1";
color=black;
a;
subgraph cluster0 {
label="Docker";
b;
}
}
subgraph cluster1 {
label="Server2";
color=black;
subgraph cluster0 {
label="Docker";
c;
}
}
}
subgraph cluster1 {
color=white;
subgraph cluster0 {
label="Server1";
color=black;
d;
}
subgraph cluster1 {
label="Docker";
color=black;
subgraph cluster0 {
label="Server1";
e;
}
subgraph cluster1 {
label="Server2";
f;
}
}
}
a -- d [penwidth=0];
b -- e [penwidth=0];
c -- f [penwidth=0];
}