Re: Network integrity and non-random removal of nodes
It still depends on the network that you are using for analysis. Assuming the paper uses the same dataset as the link Sean provided the giant cluster they are analyzing is only 8.3% of IP nodes in their sample. It takes the removal of 25% when only looking at that small densely connected section, it says nothing about what will happen to the other 91.7% of nodes. Considering that 55% of the remaining nodes are trees, they will be saying "Houston we have a problem" well before 25%. Whether or not it matters that they have a problem in an entirely different question. I've probably kicked this dead horse enough already ----- Original Message ----- From: William Waites <ww@styx.org> Date: Thursday, November 21, 2002 6:31 pm Subject: Re: Network integrity and non-random removal of nodes
"Sean" == Sean Donelan <sean@donelan.com> writes:
Sean> On 20 Nov 2002, William Waites wrote:
If you randomly select nodes to remove, by the time you have removed 25% of them, the network breaks up into many isolated islands.
Sean> One of the key points was the nodes were removed in ranked Sean> order, not in random order.
I stand corrected.
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...
So then the 12500 *biggest* routers have to be disabled before the graph breaks into many islands. This would be yet harder from an attacker's point of view, no?
-w
"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
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William Waites