F / \ D E | | B C \ / A
Suppose A is a customer of B and C.
This is possible, but only remotely probable. In the real world, D and E are likely peered, as are B and C.
"likely?" with what probability? any measurement cite please. nothing exact; something rough would be fine.
Well, the average AS Path length is something like 4, and according to the charts Geoff has presented here and there, the graph is becoming more dense, as most people interconnect. The odds of finding an end-to-end path (4 hops) on the global 'net where no-one is peered in the middle seems pretty unlikely to me. It's not impossible, but it does seem unlikely, just given the average AS Path length and the density of the graph. For example, I suppose you could make A/B/C part of the same network which is intentionally not peered, or B/C two regional providers who are not peered with one another. You could then make D/E IXPs who have no transit connectivity between them, and then make F a tier 1 provider... But this really seems unlikely to me. How would you string together 4 AS' in a row that have no connectivity to any transit AS, even regional, like this? Two hops I can see, four I have a hard time seeing.
i was hoping for measurements, not seems unlikely. as you know, i am sceptical about our internet topology intuitions and modeling given how good bgp is at hiding information and how poor our vantage points are. ripe atlas, caida, etc. give us some view, but views with inconsistencies and contradictions. we could write a paper on the hazards of as topology. oh, we did. :) randy