Giulio suggested I run a graph growth process twice, the first time with white (invisible) edges, and the second with some color (blue in this case) in order to avoid the graph displaying in crazy ways as it is being formed. It works to avoid that problem, but now, there is a second issue: the EdgeList is duplicated (double edge sword;-)). Deleting the edges upon the second pass makes the first problem come back.

Isn't there a way to control the graph display so it is less jarring, so that nodes stay fixed on the screen as edges are added