I'll mention this since no-one else has. Maple did it in the depricated deprecated network package and now does it in the plots package as graphplot3d : Make the adjacency matrix of the graph. Then the graphplot3d command will do the following: find three eigenvectors (maybe of unit length) by default for eigenvalues 2,3,4 although you can choose. This give 3 vectors in $\mathbb{R}^n$ It will view them as $n$ triples in $\mathbb{R}^3$ and use these as the vertex locations. Sometimes it works nicely showing off symmetries, other times not so well. Some documentation
I am not praising Maple here rather the method. Below are 3 plots of random sparse 50 vertex graphs. I'd like thicker edges and cuter cute balls at vertices. Also I had to fool around a bit to not have a number at each vertex.
The springs method is nice, and you can probably nudge and shake or pull and release to see what happens. At least in Maple the system of differential equations can start to really bog down for a big graph. I like that the representation by this eigenvalue method is completely determined by the graph. The resukts results can be quite nice, when it works. I tried the Hoffman Singleton Graph (50 vertices, regular of degree 7) and none of the eigenvector choices I made came out with a nice graph.
