Ya - that pretty much sums it up - interesting model dubious application in reality. Homogenous, in this context, does not mean similar platform connectivity, but nodes with same degree connecting to each other. It is more likely for a node with ten connections to connect to other nodes with ten connections than one with one or two connections. The Internet is heterogenous. So, take UUnet as your nodes at the AS level and lets say it has 1700 or so connections to other AS's. Most of those other AS's would not not also have 1700 connections, thus it is heterogenous. Lots of problems in applying that to cascading failures in reality - making AS701 disappear, BGP allowing a cascading traffic failure from "having to redistribute" AS701's traffic etc etc. Hope that makes it more clear, but it is just my interpretation of someone elses work. ----- Original Message ----- From: Douglas Denault <doug@safeport.com> Date: Saturday, February 8, 2003 3:23 pm Subject: Re: Cascading Failures Could Crash the Global Internet

I believe the answer meant heterogenous has a meaning in a statistical context. As I was a Real Variables guy I, was weak on statistics (of my day). Math guys love to use perfectly good English words giving them different meanings. Assuming that the given definition is correct, the applicability of the assumption to the backbone is still not clear to me. While not doubting the mathematical model, it seems to me there is little empirical evidence to support it in this context. Or I am in the second half of your second point.

On 8 Feb 2003, Michael Lamoureux wrote:

...

"sgorman1" == sgorman1 <sgorman1@gmu.edu> writes:

sgorman1> I believe the comments about heterogenous networks has to do sgorman1> with a measurement called assortivitiy that is used in sgorman1> statistical mechanics. A homogenous network is when nodes sgorman1> connect preferentially to nodes like them. In a sgorman1> heterogenous network they connect to nodes that are not like sgorman1> them. For networks like the Intneret and the electric grid> sgorman1> it is measured by the number of connections a node has.> sgorman1> The kicker, that the author's are alluding to, is that the sgorman1> more heterogenous a network is the more vulnerable it is to sgorman1> targeted attack. By taking out a highly connected node - sgorman1> lots of poorly connected nodes that use it as a hub are sgorman1> lost. The AS network had the highest heterogenous score of sgorman1> real-world tested networks, so lots of folks on that sgorman1> bandwagon.

I don't see how the fact that a network is homogeneous or heterogeneous has anything to do with how well connected it is. The only possible sense to this I can see is that, statistically, you are more likely to have a platform that the attacker has a viable attack for if you have lots of different platforms. But at the same time, if the attacker only has one exploit (or whatever attack vector), then you are also in a MUCH better position than someone who's network is made up 100% of that platform. I'm still not sure how having a homogeneous network helps.

Either you aren't explaining it well, or I'm being stupid. I consider> both possibilities to be equally likely at this point. ;-)

IMHO, Michael

_____ Douglas Denault doug@safeport.com Voice: 301-469-8766 Fax: 301-469-0601