According to the documentation, GraphLayout has an EdgeBundling suboption, which can take the following values:
"DividedEdgeBundling""HierarchicalEdgeBundling""StraightLine"
What does each do, what suboptions do they have, and how do I use them?
Partial answer:
"StraightLine" seems self explanatory, but not that it's not the default:

"DividedEdgeBundling" is described by István in this answer.
That leaves "HierarchicalEdgeBundling", which I cannot figure out. It seems to behave the same as "StraightLine" in naive attempts to use it.
The suboptions of these can be discovered by passing a wrong value and looking at the error message:

This also reveals that there are several more suboptions to DividedEdgeBundling than the linked post above shows.


"HierarchicalEdgeBundling"too. +1 – Silvia Oct 01 '15 at 10:21"EdgeLayout" -> {"HierarchicalEdgeBundling", "SplineWeight" -> Automatic}. – Silvia Oct 01 '15 at 10:28"SplineWeight"setting would change the "strength" of the bundling, but I haven't found a legal syntax. – Silvia Oct 01 '15 at 11:18