The automatic layout features of yEd is awesome, but it is also makes maintaining your own structure to the graph a little difficult.
I suggest giving an "anchor this node" option in the context menu, which will make that node unmoved by automatic layout algorithms. (The user can still move anchored nodes just like normal nodes.)
This would allow the user to quickly put the important nodes to positions which communicate his idea the best, anchor them, and then use yEd to elegantly reposition the less-important details.
Happy to send in some diagrams illustrating this if it helps.
Btw, awesome stuff with yEd. Loving it to bits.