Here's a little back-of-the-envelope calculation. From a recent Everything Daily Report (as I go to check my email) there were 3,719,603 links, and 287,745 nodes. (I am using commas for readability because the numbers are large.) This is, on average, 12.9 links *per node* (which may include multiple writeups). This seems kind of low when you think about it, but it points out how rough this estimate will really be: the distribution of links/node is probably closer to bimodal than normal: there are lots of pithy writeups with only a handful of links, and also lots of meaty writeups with tons of links. This is especially true because a large percentage of our writeups are Webster 1913's (98,233 of these, or roughly 1/4 of all writeups!) which tend to have *very few* hardlinks.

We also have to allow for the fact that a certain percentage of links, as we all know, lead nowhere. Assume for the sake of argument that this is maybe 20% of all hardlinks. Then the expected number of nodes you can possibly reach from a single node is (12.9 * 0.8)^6, or 1,219,312. That's pretty encouraging, because it's way more than we have.

But that number is too high, because it assumes that there are no cycles in our directed graph. (Here I am using "graph" as in graph theory.) If you think of this as a tree rooted at a particular node, lots of nodes at level n of the tree will have links back to nodes on the same level or lower, which ultimately makes the tree less bushy, and reduces the number of nodes the tree finally reaches. If we go with 10.3 as our working link number (12.9 * 0.8 from before), the probability that any node on level n of the tree will not refer back to the others, to leading order, is (1 - (10.3^n)/287,745). So the percentage of the 1,219,312 unique nodes we expect to end up with is roughly the product of these, for n = 1 to 5 (we get the first link for free assuming the node isn't self-referential). That product is about 0.57, so the actual number of nodes we expect to get to taking into account dead links *and* recombination in the tree is 0.57 * 1,219,312 = 695,007.

This is well beyond the 287,845 nodes we actually have, suggesting that we don't have enough statistical information (i.e. a complete distribution) about the inter-linkedness of E2 to be sure. But because we have overshot it is suggestive that 6 is enough almost all of the time, which is all we can really hope for with a B.O.E. calculation anyway.