How do I impose the y position on a node when using graphviz to draw lattices?

Question

I am using Graphviz to draw a lattice.
The nodes are set of numbers.

Being a lattice, I would like the height position (the y) of a node to represent the number of elements in the set represented by the node. Then the x position should be defined by graphviz to make the representation cleaner.

Is it possible?

According to the dot documentation there should be the attribute pos that should define the position of a node. But although I tried many times in many different ways I could not get any graph where the position of a node was defined. Did anyone had any success with this?

What follows is the classical dot file I use:

digraph G {
"528 544\n640 768" -> "768 528"; 
"528 536\n530 539" -> "539"; 
"528 536\n530 539" -> "528"; 
"800 896 548\n944 566 728\n539 704 768" -> "704 768\n539 548"; 
"800 896 548\n944 566 728\n539 704 768" -> "944 728\n539 566"; 
"800 896 548\n944 566 728\n539 704 768" -> "944 800\n896 768"; 
"768 539" -> "768"; 
"768 539" -> "539"; 
"768" -> "∅"; 
"944" -> "∅"; 
"944 528 536\n530 566 560\n728 656 539" -> "528 536\n530 539"; 
"944 528 536\n530 566 560\n728 656 539" -> "944 728\n539 566"; 
"944 528 536\n530 566 560\n728 656 539" -> "944 656\n528 560"; 
"704 768\n539 548" -> "768 539"; 
"944 728\n539 566" -> "944"; 
"944 728\n539 566" -> "539"; 
"800 896 640\n944 560 528\n544 656 768" -> "528 544\n640 768"; 
"800 896 640\n944 560 528\n544 656 768" -> "944 656\n528 560"; 
"800 896 640\n944 560 528\n544 656 768" -> "944 800\n896 768"; 
"539" -> "∅"; 
"944 656\n528 560" -> "944"; 
"944 656\n528 560" -> "528"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "800 896 548\n944 566 728\n539 704 768"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "944 528 536\n530 566 560\n728 656 539"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "800 896 640\n944 560 528\n544 656 768"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "768 704 548\n528 530 544\n536 640 539"; 
"768 528" -> "768"; 
"768 528" -> "528"; 
"528" -> "∅"; 
"768 704 548\n528 530 544\n536 640 539" -> "528 544\n640 768"; 
"768 704 548\n528 530 544\n536 640 539" -> "704 768\n539 548"; 
"768 704 548\n528 530 544\n536 640 539" -> "768 528 530\n539 536"; 
"944 800\n896 768" -> "768"; 
"944 800\n896 768" -> "944"; 
"768 528 530\n539 536" -> "528 536\n530 539"; 
"768 528 530\n539 536" -> "768 539"; 
"768 528 530\n539 536" -> "768 528"; 
}

If anyone could write an example of a file where the height of one node was defined I would be very grateful.

Answer 1

I found the answer.

Here: http://www.linuxdevcenter.com/pub/a/linux/2004/05/06/graphviz_dot.html?page=2

Essentially it is possible to define what sets of nodes should be at the same hight. TO get the nodes A and B at the same hight I need to add the line: {rank=same; A B };

So here is a similar example as the one before, but with the nodes set up right:

digraph G {
{rank=same;  "768"  "944"  "539"  "528" };
{rank=same;  "768 539"  "768 528" };
{rank=same;  "768 640\n528 544"  "528 536\n530 539"  "768 704\n539 548"  "944 728\n539 566"  "944 656\n528 560"  "944 800\n896 768" };
{rank=same;  "800 896 548\n944 566 728\n539 704 768"  "528 944 536\n530 566 560\n728 656 539"  "800 896 944\n656 560 528\n544 640 768"  "768 640 548\n528 530 544\n536 539 704" };
"768 640\n528 544" -> "768 528"; 
"528 536\n530 539" -> "539"; 
"528 536\n530 539" -> "528"; 
"800 896 548\n944 566 728\n539 704 768" -> "768 704\n539 548"; 
"800 896 548\n944 566 728\n539 704 768" -> "944 728\n539 566"; 
"800 896 548\n944 566 728\n539 704 768" -> "944 800\n896 768"; 
"768 539" -> "768"; 
"768 539" -> "539"; 
"768" -> "∅"; 
"944" -> "∅"; 
"528 944 536\n530 566 560\n728 656 539" -> "528 536\n530 539"; 
"528 944 536\n530 566 560\n728 656 539" -> "944 728\n539 566"; 
"528 944 536\n530 566 560\n728 656 539" -> "944 656\n528 560"; 
"768 704\n539 548" -> "768 539"; 
"944 728\n539 566" -> "944"; 
"944 728\n539 566" -> "539"; 
"800 896 944\n656 560 528\n544 640 768" -> "768 640\n528 544"; 
"800 896 944\n656 560 528\n544 640 768" -> "944 656\n528 560"; 
"800 896 944\n656 560 528\n544 640 768" -> "944 800\n896 768"; 
"539" -> "∅"; 
"944 656\n528 560" -> "944"; 
"944 656\n528 560" -> "528"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "800 896 548\n944 566 728\n539 704 768"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "528 944 536\n530 566 560\n728 656 539"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "800 896 944\n656 560 528\n544 640 768"; 
"896 640 656 536\n530 728 539 704\n768 800 544 528\n548 944 566 560" -> "768 640 548\n528 530 544\n536 539 704"; 
"768 528" -> "768"; 
"768 528" -> "528"; 
"528" -> "∅"; 
"768 640 548\n528 530 544\n536 539 704" -> "768 640\n528 544"; 
"768 640 548\n528 530 544\n536 539 704" -> "768 704\n539 548"; 
"768 640 548\n528 530 544\n536 539 704" -> "528 768 530\n539 536"; 
"944 800\n896 768" -> "768"; 
"944 800\n896 768" -> "944"; 
"528 768 530\n539 536" -> "528 536\n530 539"; 
"528 768 530\n539 536" -> "768 539"; 
"528 768 530\n539 536" -> "768 528"; 
}