I have been working on characterizing the internet hierarchy. I noticed that 27% of the total possible tier-2 provider node pairs are not connected i.e., they dont have any tier-1 node connecting them nor a direct peering link between them.
It's quite simple. The Internet is not a tree hierachy; it is a partial mesh. Partial meshes can often be characterised as having some sort of hierarchy of connectedness, however the Internet does change continuously which means that an analysis of hierarchy done today will come up with different results from last year's analysis. The terminology of "tier 1" and "tier 2" only refers to a brief time in the evolution of the Internet in North America during the 1990s when the topology was much more treelike. That is all changed. Go to google and search the following line exactly as written. "internet topology" "partial mesh" --Michael Dillon