First off, I love this application.
I think it would be very beneficial to add an option to be able to move a Parent bubble and leave its Children in their current position.
Being able to move a Parent with all its dependencies is excellent, but sometimes having the option to only move the Parent is also great for rearranging layout without messing the whole complex mind map. Some of us are a little cuckoo (me) and a lot is going on in our minds. When we have to add and suddenly there isn't much space due to some Parent having too much space and moving that Parent just a little could ease to progress without having to move everything.
Just my two cents.