How to Visualize a Graph

You need two things to make a graph sort itself a visual appealing way.

A spring force between every two nodes connected by an edge. I use a spring that wants to maintain a distance of one and has a strength of one.
A repellent force between every two nodes. I use a spring that has a strength of 0.02 and wants to maintain a distance of 50.

The Algorithm:
Note: My version of this code is about 30 lines, and it could be smaller.

Copy all of the existing X and Y values for each node into the array Xnew and Ynew
For each node I
- For each node J
  - if (i == j) skip this iteration
  - If (I is in the same place as J)
    - Move change newX and newY a bit
  - else
    - compute a springX and springY for length 50 with strength 0.02
    - If there is an edge, add a springX and springY for length 1 with strength 1.0
  - Update newX and newY based on springX and springY
copy newX and newY into X and Y

How to model a spring:
The force of a spring of length LENGTH is given by CONSTANT * (LENGTH - DISTANCE) Points:

10 -- Can have the graph evolve nicely
5 -- Only one pair of array copies per itearion.
5 -- No array copies per iteration.
-2 -- Per day after Wed March 24

Double Buffering:
See http://euclid.nmu.edu/~randy/Classes/CS120a/DoubleBuffering/ for a how-to. You probably won't need this. The source.