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Re: Cascading Failures Could Crash the Global Internet
From: <sgorman1 () gmu edu>
Date: Sat, 08 Feb 2003 17:34:11 -0800

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 

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 
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 
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.   


Douglas Denault
doug () safeport com
Voice: 301-469-8766
 Fax: 301-469-0601

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