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?).