Googling for hierarchical edge bundling gives very interesting pictures though. Can we actually have something like this visualization in Mathematica using this option?
The "HierarchicalEdgeBundling" edge layout seems to automatically imply a certain vertex layout (and ordering) as well.
This can make very pretty images, I do wonder why it’s never shown in the documentation. I tried to figure out this option several times during the past few years, and I never managed to get it to work because every time I made the same mistake: I also specified a vertex layout.