the long-tailed
degree distribution structure of
real-world complex networks
has implications for their robustness
for example since these networks are
largely structured around
hubs they're vulnerable to targeted hub
failure an example of this is
on the web when large
highly connected websites are targeted
by malicious people via attacks
called distributed denial of service
attacks
now if my web page goes down nobody's
really going to get
upset because it doesn't have a lot of
links coming into it whereas if a big
website like
yahoo goes down a very highly connected
website
that's going to cause a lot more havoc
on the web
that's true in all networks that have
this kind of hub structure
we talked about this for instance with
respect to airline networks
where if a hub city is having bad
weather
causing flights to be delayed that's
going to have effects that percolate
throughout the system
similarly in biological networks the
extinction of a hub
species whether it be a predator or
a prey species in a food web is going to
have huge implications
for the entire food web the same thing
goes
for other kinds of biological networks
and it may be that a network approach to
thinking about
biology is going to end up being more
important
for understanding health and well-being
than
than the genetic sequencing of the human
genome project
although these networks are vulnerable
to targeted hub failure they're also
robust to random node failure
if a single node becomes unusable for
some reason
since most nodes have very low degree
it's not going to have a big effect on
the network
in the internet for example internet
servers are going
down all the time being taken out of
commission for temporary periods
but because of the long-tailed structure
of these networks such random node
failure
failure often doesn't have much of an
effect
unless nodes can cause other nodes to
fail and then we can get something
called cascading failure
an example the power grid
here's a satellite picture of a region
in the northeast
u.s and canada before and after a huge
electrical blackout that occurred in
august 2003
evidently a power station in ohio
got overloaded because of a downed power
line
it transferred its load to another power
station
that itself got overloaded and shut down
and so on in a kind of domino effect in
which there was a cascade of failures
bringing out bringing down a lot of the
electrical
grid of the northeastern united states
you can see before the blackout lots of
lights here
much diminished here on the day of the
blackout
so that's a common example of a
cascading failure
cascading failure can also affect
economic systems
such as banks and you can see here in
the years from 2007
to 2010 a sort of domino effect of banks
failing
once one bank fails its causes and
effect
throughout the bank network if the bank
network is closely interconnected and
has this
cascading failure possibility we can get
this kind of cascade of
bank failures and we see similar
patterns of cascading failures and all
kinds of systems ranging from
the body to ecological systems to
computer and communication networks
wars and so on
now i want to talk a little bit about
the implications of the long-tail
distribution for
thinking about risk
it's been traditional to model risk
using normal distributions or these bell
curve
distributions these are different shapes
of of these normal distributions you can
see some of them have high peaks some of
them have lower peaks
and wider and so on but all of them have
the feature that events in the tail of
the distribution are highly unlikely
however if you look at a long tail
distribution
like this one it turns out that
events in the tail are more likely than
a normal distribution
sometimes much more likely so if you're
thinking about
risk for instance in a financial market
housing market and any kind of economic
system
or even earthquake risk or something
like that
if your underlying model is a normal
distribution a bell curve
you're going to assume that
risks out in the tail have very low
probability
but if your model was actually one of
these long tail distributions
you would be much more concerned about
possible risks because they'd have a
higher probability
some people have called this situation
the long tail distribution more normal
than
normal because they're so common in
complex networks that are ubiquitous in
all kinds of different domains
this sort of thinking was behind paul
krugman's
quote in the new york times in 2009 paul
krugman being
a nobel prize-winning economist and he
said few economists are
current crisis coming but this
predictive failure was the least of the
field's problems
more important was the profession's
blindness to the very possibility of
catastrophic failures in a market
economy
so he's talking right there about what
people think about the tales of these
distributions
these risk distributions how much
probability
is down here well there's a lot more
if you assume that you have a power law
or other long-tail distribution
than if you have a normal distribution
and what krugman is saying
is that the profession of economics
was probably more fixated on modeling
risk
and other factors using normal or
gaussian distributions
whereas they should have been using
these more long-tailed distributions
you've all seen the phrase too big to
fail
with respect to large banks or other
financial institutions but an
alternative idea
put forth in an editorial by duncan
watts
is that instead of worrying about things
that are too big big to fail
we should worry about institutions that
are too complex to exist
because complexity seems to produce such
power law or long-tail distributions
rather than normal distributions and in
this article
watts talks about how the power grid
economic systems bank networks and so on
can become
so complex that catastrophic failure
is sometimes inevitable because of the
long
tail of risk well let's end with another
quote from duncan watts
so far in this lecture we've focused on
structure of networks we've looked at
small world structure
scale-free and long-tailed degree
distributions
and so on we haven't really talked much
about
dynamics on networks so duncan says
next to the mysteries of dynamics on a
network
whether it be epidemics of disease
cascading failures and power systems
or the outbreak of revolutions the
problems of networks that we have
encountered
up to now are just pebbles on the
seashore
well duncan said this 10 years ago and
within the last 10 years a huge amount
of work has been done
on studying how dynamics occur on
networks
how information spreads how epidemics
occur
how cascading failures happen we're not
going to cover that
those topics in this course but
hopefully in a future course
and i'd also like to mention that on the
course materials page
there's many references that talk about
what's been happening in the last
10 years of network science in terms of
dynamics particularly that you might
find interesting