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I find GraphViz easy to use, but it renders 2D graphs. Is there an equivalent that renders 3D graphs? The nodes could stay 2D but the graph as 3D would be great. If not, is there an alternative such as using a Perl module or Java package?
My searches only result in 3D gaming engines.
There is not a great interactive tool I know about, but you can generate a 3D layout in Pajek and then use the King viewer in a website. You can see an example in this YouTube video, with a screenshot here:
Just so you know, while 3D graph visualizations look pretty they are actually quite poor at showing graph structure due to lots of occlusion. This is even worse for a static image with no interaction. I would highly suggest using a good 2D graph visualization system like Gephi, NodeXL, or Cytoscape. Disclaimer: I am an advisor for the NodeXL project.