DAGs vs Trees

As I wondering whether or not there is a better layout algorithm for the module browser window, I looked into tree maps. Of course, the modules in a program form a DAG, not a tree, so I wondered just how big the tree would get if all of the shared structure in the DAG were replicated. Hey, I figured, if a tree map can handle showing me my entire filesystem, maybe that could work.

... yeah, no. Turns out to be hopeless. In the spirit of a geeky take off on a jelly bean counting contest, lets see if you can guess just how big these things get. Consider the module graph from the program #lang scheme (ie, the graph that just contains an empty program). This program loads 170 modules with 917 connections between modules (counting the main file that just contains the #lang scheme).

So, the question: how many nodes are there in the unsharified tree? First one to come within 1 billion of the right answer gets all of the fame and glory that this blog brings to bear (har har). I'll post the answer in the comments in a few days (and no fair cheating, those of you that know enough to be able to get your hands on the DAG).