I believe the comments about heterogenous networks has to do with a measurement called assortivitiy that is used in statistical mechanics. A homogenous network is when nodes connect preferentially to nodes like them. In a heterogenous network they connect to nodes that are not like them. For networks like the Intneret and the electric grid it is measured by the number of connections a node has. The kicker, that the author's are alluding to, is that the more heterogenous a network is the more vulnerable it is to targeted attack. By taking out a highly connected node - lots of poorly connected nodes that use it as a hub are lost. The AS network had the highest heterogenous score of real-world tested networks, so lots of folks on that bandwagon. That said I don't think the tolerance parameter they set up in the paper makes much sense when applied to the Internet at the AS level. Basically it says once traffic exceeds a certain threshold the node will fail and cause cascades across the network. You guys are the experts but that does not sound overly realistic. ----- Original Message ----- From: Douglas Denault <doug@safeport.com> Date: Saturday, February 8, 2003 7:31 am Subject: Re: Cascading Failures Could Crash the Global Internet

The model proposed makes several assumptions. My question is about:

Many real-world networks are heterogeneous and as such are expected to undergo large-scale cascades if some vital nodes are attacked.

on page 3. I do not get the basis for this assumption. So any help for a 60's educated math major would be appreciated.

On Thu, 6 Feb 2003 sgorman1@gmu.edu wrote:

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The paper is avaibable on the Los Alamos site free of charge:

http://xxx.lanl.gov/PS_cache/cond-mat/pdf/0301/0301086.pdf

----- Original Message ----- From: Sean Donelan <sean@donelan.com> Date: Thursday, February 6, 2003 12:43 pm Subject: Cascading Failures Could Crash the Global Internet

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Sigh, there are differences between tightly coupled networks,

such as

...

...

the electric power grid and loosely couple networks like the Internet. But there are also some similarities, such as electric grids use DC interconnections to limit how far AC disturbances propagate; the Internet uses AS interconnections to limit IGP disturbances from propagating.

http://sci.newsfactor.com/perl/story/20686.html

The actual article requires payment to read http://ojps.aip.org/getabs/servlet/GetabsServlet? prog=normal&id=PLEEE8000066000006065102000001&idtype=cvips&gifs=Yes

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