One example of the implications is the
fact that Google works so well. And that

can be explained by the fact that the web
has a long-tailed degree distribution

instead of a bell curve degree
distribution.

Google is able to rank its pages that that
it responds to for your query by giving

preference to webpages that have many
inlinks. That is, many other webpages

point to them. Google assumes that if a
webpage has many pages that point to it,

then it's more likely to be a good
response to your query. It's more likely

to be, say, authoritative. The reason this
works is because at every level of the

network, you have some pages that have
many links to them, and many other pages

that have few links to them. So, no matter
what your query, Google will be able to

find pages that have relatively many
links to them, and thus can put them high

up in the list. Whereas if the web was a
random network, then all of the webpages

would have about the same number of
links, the average of the bellcurve. And

Google would have no way to discriminate
among them to decide how to rank the

answers. Now, the web was not designed by
anyone. It built itself.

It's self-organized. And it just happened
to self-organize in this way, so that it

has this kind of long-tailed degree-
distribution, and Google took advantage

of that. This same notion explains some
of the success of other networks in nature

The fact that they have long-tailed
distributions is taken advantage of and

becomes useful for organisms, and social
systems, as well.

You can read about that in some of the
suggested readings on the course materials

website.

The obvious question is how does this
structure of scale-free networks arise?

If the web wasn't designed by any person
or committee of people to be that way,

how did it become that way? 
Well, there's multiple hypotheses:

One prominent hypothesis is called
preferential attachment. It's the idea

that the rich get richer. That is, if
you're coming in, and you have a new

webpage, and you want to decide who to 
link to, you're more likely to link it to

a page that already has a lot of links to
it, just because that page is more likely

to be found by you.

Similarly, the next time somebody else
comes along and wants to link to a page,

that page will be even more likely to be 
linked to, because now you've linked to

it, and so the number of links to it have 
increased. And so on. So this is the

idea, the rich get richer; the linked to 
get more linked to; the cited get more

cited-that happens in science, at least. 
And by cited, I mean c-i-t-e-d. That is,

many people cite the papers that have 
already been cited by many people. We're

going to be looking at a NetLogo model of 
preferential attachment. And here's how

that model works: We start with two 
linked nodes. At each time step, we

create a new node. The new node is going 
to randomly choose one of the existing

nodes to link to. But it has bias: the 
more links the existing node has, the

more likely it is to be chosen. For 
example, each one of these existing nodes

has one link coming out of it. And so, 
each has an equal chance here of being

linked to by this node. So let's say that 
this node randomly chooses this other

node to link to. Ok, at the next time 
step, we have a new node, and it has a

choice to make, but this node in the 
middle here has two links coming out of

it, whereas each of these other nodes has 
one link, so the nodes with one link only

have a 25% chance of being picked, 
whereas the node with two links has a 50%

chance of being picked. And here, this 
node picked it. And this continues, so

let's see what that model looks like. 
Here's the interface for

PreferentialAttachment.nlogo, which is 
one of the models in the NetLogo models

library, so you can get it there, or else 
you can download it from our course

materials page. So I'm going to 'setup', 
and if I 'go' once, we have our third

node comes in, and the links to that 
node. 'Go' once again, again, again,

again, again. Well, you're going to see 
that this is going to start to look kind

of messy. In fact, if I keep going, I get 
a big mess. But this has a nice feature,

which is you can click 'layout' on, and 
now if I do 'setup', and 'go', it

actually creates a very nice layout for 
the network. Although it's a little bit

slower to run. So you can see this is 
going, just doing that bias choice each

time a new node is created. It makes a 
bias choice among the nodes that exist.

You can see that there's a big hub 
forming here in the middle, and little

hubs down here, and inside the little 
hubs, there's even littler hubs, and so

on. And if we just let this run, it's 
going to turn into a very nice scale-free

network. And you can see the degree 
distribution here, which has the

characteristic power law-looking shape, 
and when it's plotted on a log-log plot

here, it's making a straight line. And as 
more and more nodes are added, these will

look more and more like actual power 
laws. So this model is more to look at

rather than to actually do experiments 
with, but I recommend downloading it from

the course materials page, and playing 
with it. The interesting thing here is

that such a very simple model of network 
formation can produce networks that look

very much like real world networks. So 
there might be something to this

hypothesis of how these kinds of networks 
form.