Adding labels under subgraphs in Graphviz - graphviz

Question

I use the following code to produce a graph using dot in Graphviz. I have manually included the coordinates of nodes, as I require four disjoint subgraphs placed adjacent to one another, as in the picture.
I would love to add labels under each of the subgraphs: $G_0$, $G_1$, etc. Adding label under subgraph creates a box and ignores my coordinates alignment. Is there any other way, like placing arbitrary text at specified coordinates? I use "dot -Teps -Kfdp -n trees -o t.eps" for compilation.
digraph Trees {
node [shape=circle, style="filled", fixedsize=true,width=0.6]; 0; 1;2; 3;4; 5;6; 7; 8;9;10;11;12;13;14;15;
0[pos = "0,1!"]
1[fillcolor=red, pos = "-1,2!"]
2[pos = "1,2!"]
3 [pos = "0,-0.5!"]
5[label=1, fillcolor=red, pos = "2,2!"]
4[label=0, fillcolor=red, pos = "3,1!"]
6[label=2, pos = "4,2!"]
7[label=3, pos = "3, -0.5!"]
9[label=1, fillcolor=red, pos = "5,2!"]
8[label=0, fillcolor=red, pos = "6,1!"]
10[label=2, pos = "7,2!"]
11[label=3, fillcolor=red, pos = "6, -0.5!"]
12[label=1, fillcolor=red, pos = "8,2!"]
13[label=0, fillcolor=green, pos = "9,1!"]
14[label=2, pos = "10, 2!"]
15[label=3, fillcolor=green, pos = "9, -0.5!"]
overlap=false;
fontsize=10;
subgraph 1{
edge [dir=none] 1->0 2->0 3->0;
}
subgraph 2{
edge [color=red] 5->4;
edge[color=black, dir=none] 6->4 7->4;
}
subgraph 3{
edge [color=red] 9->8 8->11;
edge [color=black, dir=none] 8->10;
}
subgraph 4{
edge [color=green] 12->13; 13->15;
edge [color=black, dir=none] 13->14;
}
}

Answer 1

The sub-graphs can be made disjoint using clusters and the dot layout engine. The same approach will also permit the introduction of cluster labels. They can be placed at the bottom of the cluster as required without creating dummy nodes.
This way, no absolute positions are required, and, the layout is automatically generated even if other nodes are added. The exact position of the nodes change, but the graphs remain topologically unchanged.
digraph Trees { node [shape = circle, style = "filled", fixedsize = true, width=0.4];
edge [dir = none];
layout = dot; overlap = false; fontsize = 10;
graph [labelloc = "b", penwidth = 0];
{ node [fillcolor = "red"];
1; 5 [label = 1]; 4 [label = 0]; 9 [label = 1];
8 [label = 0]; 11 [label = 3]; 12 [label = 1];
}
2; 0; 3; 6 [label = 2]; 7 [label = 3];
10 [label = 2]; 14 [label = 2];
{ node [fillcolor = "green"];
13 [label = 0]; 15 [label = 3];
}
subgraph cluster1{
label = "Subgraph 1";
{ 1; 2; } -> 0 -> 3;
}
subgraph cluster2{
label = "Subgraph 2";
5 -> 4 [color = red, dir = fwd];
6 -> 4 -> 7;
}
subgraph cluster3{
label = "Subgraph 3";
9 -> 8-> 11 [color=red, dir = fwd];
10 -> 8 [color=black];
}
subgraph cluster4{
label = "Subgraph 4";
12 -> 13 -> 15 [color=green, dir = fwd];
14-> 13;
}
}

Answer 2

Instead of using explicit node positions, you may use a simple directed graph combined with some rank constraints, invisible edges and text nodes instead of subgraph labels:
digraph Trees {
fontsize=10;
node [shape=circle, style="filled", fixedsize=true,width=0.6];
{rank=same;
a1[label=1, fillcolor=red];
a2[label=2];
a3[label=1, fillcolor=red];
a4[label=2];
a5[label=1, fillcolor=red];
a6[label=2];
a7[label=1, fillcolor=red];
a8[label=2];
}
node[label=0];
b1;
b2[fillcolor=red];
b3[fillcolor=red];
b4[fillcolor=green];
node[label=3];
c1;
c2;
c3[fillcolor=red];
c4[fillcolor=green];
node[shape=none, fillcolor=transparent];
d1[label="Label 1"];
d2[label="Label 2"];
d3[label="Label 3"];
d4[label="Label 4"];
edge[dir=none];
a1->b1;
a2->b1;
b1->c1;
c1->d1[style=invis];
a3->b2[dir=forward, fillcolor=red, color=red];
a4->b2;
b2->c2;
c2->d2[style=invis];
a5->b3[dir=forward, fillcolor=red, color=red];
a6->b3[dir=forward, fillcolor=red, color=red];
b3->c3;
c3->d3[style=invis];
a7->b4[dir=forward, fillcolor=green, color=green];
a8->b4[dir=forward, fillcolor=green, color=green];
b4->c4;
c4->d4[style=invis];
edge[style=invis];
a2 -> a3;
a4 -> a5;
a6 -> a7;
}