Are there any existing libraries that can handle this problem?

I tried using the physics library, but encountered some problems. I made all nodes repulse each other, and placed springs with varying strength where the edges should be. However, the springs freak out for highly connected graphs. I also looked into using GraphViz for computing x and y-coordinates for my nodes, but this will involve a lot of extra script writing that I'd rather not do...

Any thoughts much appreciated!