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Title says it: I am wondering what "BGP graphs" (e.g. the ones on Hurricane Electric or robtex) show exactly? Another example can be found here on superuser: Is there a way to test alternate IPv4 routes?

I would expect the websites to explain it somewhere but until now I could not find that information.

I know what BGP is (roughly). And I think the graphs show, starting with a certain AS, what peers that AS' border gateways have (i.e. what AS' it is peering with) and then what AS' these AS' are peering with and so on.

But what I don't understand are things like why are there arrows of different "stroke size" and how do they decide/know when to "stop" (i.e. there are always more peerings and the graph would go on an on until all AS' and peerings of the internet is depicted, no?).

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Since these sites don't explain the technologies behind the websites I can only guess, but I think that my guess is pretty accurate.

You are right about these graphs purpose. They are indeed show "starting with a certain AS, what peers that AS' border gateways have and then what AS' these AS' are peering with and so on"

Arrows of different strokes show the "amount of traffic" going from AS' peers to itself. The bigger the stroke size, the more amount of traffic is going through the peer. Hurricane Electric determines this, by looking in the second AS in the AS_PATH of AS' prefixes on several BGP routers that located in different places.

How they decide when to stop? If you look at the graph carefully you will see that all of the last AS on the graph are Tier-1 or major networks that mistakenly believed to be Tier-1. You can read more on the topic here Tier-1 networks

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I see your point with the Tier 1 networks, that's interesting, thanks. But then DTAG and Tata are considered Tier 1 too but the example HE graph goes on after them nevertheless. –  scherand Mar 18 '13 at 21:16
    
Yes, it goes on after them, but only to other Tier 1 networks. You can see that with some simpler graph AS35233 –  Rostyslav Fridman Mar 19 '13 at 9:44
    
The broad-stroked arrows might be the Autonomous Systems that are providing transit (a function similar to a router's default gateway) to HE.net... –  Nevin Williams May 24 '13 at 19:38

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