Re: Network integrity and non-random removal of nodes
The supposition would be that the remaining nodes are evenly distributed around the core so the percentage of nodes outside of the core without connectivity should be roughly the same as the percentage of nodes removed from the core. At least until the core goes non-linear...
Is that the supposition stated in the paper? The reason being it contradicts quite a bit of similar research. Nodes inside and outside of the core do not typically disconnect at the same rate. Think of it this way, if a big well connected node goes down the other big conencted nodes in the core are likely to have an alternate connection to compensate for the link loss. Average distance might go up a little bit, but that is about it. The nodes outside of the core on the other hand are much more sparsely connected. 55% of them are trees meaning that they only have one connection. There is no back up link, so if their big hub node goes down they are out of commission. Hence you could have large numbers of nodes outside the core disconencted before you would see any effect inside the core. By the time the core goes non-linear the periphery is gonna be long gone and disconnected. ----- Original Message ----- From: William Waites <ww@styx.org> Date: Thursday, November 21, 2002 7:14 pm Subject: Re: Network integrity and non-random removal of nodes
"Sean" == <sgorman1@gmu.edu> writes:
Sean> it says nothing about what will happen to the other 91.7% of Sean> nodes. Considering that 55% of the remaining nodes are Sean> trees, they will be saying "Houston we have a problem" well Sean> before 25%.
The supposition would be that the remaining nodes are evenly distributed around the core so the percentage of nodes outside of the core without connectivity should be roughly the same as the percentage of nodes removed from the core. At least until the core goes non-linear...
It would be interesting to see what outdegree looks like as a function of rank -- in the paper they give only the maximum and average (geo. mean) outdegrees. Is there also a critical point 25% of the way through the ranking? Probably not or one would expect they'd have mentioned it...
It turns out that this is buried in one of the graphs (fig. 6) and does not appear to have any special properties 25% of the way through. It does have an inflection point around the 1000th node or so (2.5%).
-w
"Sean" == <sgorman1@gmu.edu> writes:
>> The supposition would be that the remaining nodes are evenly >> distributed around the core so the percentage of nodes outside >> of the core without connectivity should be roughly the same as >> the percentage of nodes removed from the core. At least until >> the core goes non-linear... Sean> Is that the supposition stated in the paper? No. Sean> The reason being it contradicts quite a bit of similar Sean> research. Nodes inside and outside of the core do not Sean> typically disconnect at the same rate. References? Note that I posited that the rate was proportional, not the same. Sean> The nodes outside of the core on the other hand are much Sean> more sparsely connected. 55% of them are trees meaning that Sean> they only have one connection. There is no back up link, so Sean> if their big hub node goes down they are out of commission. That's more or less what I said. If the trees are evenly distributed around the core, and you take away 2% of the core, you can expect 2% of the trees to disappear too. Of course 2% of the trees is a much larger number of nodes than 2% of the core. Sean> Hence you could have large numbers of nodes outside the core Sean> disconencted before you would see any effect inside the Sean> core. By the time the core goes non-linear the periphery is Sean> gonna be long gone and disconnected. True iff the links to the periphery are not evenly distributed across the core, which is my, perhaps faulty, underlying assumption. Does UUNet still own most of the trees? -w
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William Waites