laying out a large graph with graphviz

My daughters have made a game not unlike tic-tac-toe. Of course as I played it with them I started brute-forcing it in my head...

So at lunchtime I made a quick little Python script to 'solve' the game. And I wanted to see the results graphically, so I generated a dot file of all legal moves:

I've pasted the data here.

When I try and render it using dot, it takes forever and I abort it after a few hours.

If I render it using neato or sfdp etc, it takes a few seconds or less but the layout is impossible to actually read:

sfdp -x -Tpng data.dot > data.png

neato -x -Tpng data.dot > data.png

I would be happy for the resulting image to be several megapixels.

How can I lay out and render such a big graph? I am open to non-dot suggestions, like Python libraries that can do the layout too.

^{(somewhat related link)}

Added: my Python script to solve the game and generate the dot file

Try this:

sfdp -x -Goverlap=scale -Tpng data.dot > data.png

The -Goverlap preserves the layout but uniformly scales things up until there are no more node overlaps. I was able to get a ~77MB PNG that looks like this when you zoom out.

you could still use the neato but modify the .dot file putting: [splines=true overlap=false]

And your file should look like this:

digraph luffarschack {
    graph [splines=true overlap=false];
    node [shape=none]; 
        ...here your nodes;
        ...here your edges;
}

It should work if you just put in the second line "graph [splines=true overlap=false]" and everything else remains the same.

In addition to other answers, you may use other tools like Gephi.

Gephi is the leading visualization and exploration software for all kinds of graphs and networks. Gephi is open-source and free.

Runs on Windows, Mac OS X and Linux.

I found dot with the default -Kneato too slow on my large graph (svg). I ended up using

dot -Ksfdp -ooutput.svg -Tsvg input.dot

where input.dot was

digraph {
    graph [overlap=false];
    a -> {b c d e f g}
    b -> {c e g x f}
    ...
}