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Which visualisation software for a layered graph?

I have produced a CSV file in the following format:

position number | list of positions it links to | 2nd list of positions it links to | ... | 6th list of positions it links to 

All the items are integers and the lists are of varying size.

The file forms a kind of tree or web (it's a game tree).

I would like to visualise the data as a web or tree.

I can sort the tree according to distance from opening move (another integer), but maybe I won't need to.

I would like it to look something like this:

1
| \
2  4
|\ |\
3,7,5,9
......
....
|/
2000

Any ideas on what software I should use and a few hints?