> automate creating images of them without edges having to cross each other, etc.

Really? I have doubts it's always possible to draw a planar graph.

consider a 3d-cube, how do you want to draw a planar graph without crossings - here x ?

There are two basic cases where the graphs cannot be embedded in a 2-d representation without crossing lines:

  1. 3 nodes that are each fully connected w/ 3 other nodes 
    a -> A, B, C
b -> A, B, C
c -> A, B, C

    [download]
  2. 5 densely connected nodes 
    A -> B, C, D, E
B -> C, D, E
C -> D, E
D -> E

    [download]
All graphs that can't be embedded in a 2-d plane have those cases embedded in them.

Your cube example actually can be embedded. You just lose the pretty perspective (or gain a new one...). 

      0
    / | \
   /  |  \
  /   B   \
 /   / \   \
A---a   c---C
 \   \ /   /
  \   1   /
   \  |  /
    \ | /
      b

[download]
This is proven by Kuratowski's theorem and is discussed here.

#11929 First ask yourself `How would I do this without a computer?' Then have the computer do it the same way.

In reply to Re^3: Visualizing a dependency graph in a web page by kennethk
in thread Visualizing a dependency graph in a web page by LanX

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