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Hi. In this set of lectures, we're gonna
talk about networks. Networks have become

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an incredibly popular topic for a variety
of reasons. One is, the internet has

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allowed us to make all sorts of network
connections with people, and to give us

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graphs of those networks. We're just more
aware that networks exist. Another thing

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is that we get more and more data on
networks. We're getting to see the

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importance of networks for all sorts of
things, Whether it's scientific

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innovation, whether it's the spread of
ideas, Whether it's the polarization of

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critical thought, And whether it's the
rise of. With a decrease in smoking with a

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rise in social trends, You can see these
effects through networks using new

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techniques. What we want to do in this set
of lectures is understand a little bit

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about how networks work and why they're so
important. So first thing I just want to

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convince you the networks have become a
hot topic. So what I'm gonna do is I'm

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gonna pull up a couple of graphs from
Google N Gram and what this does is it

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looks at the frequency at which words are
used Over time. So, they basically

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scanned, they've scanned in millions of
books and this tells you the frequency of

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particular words. So, the first word we're
gonna look at is interstate. So, this

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would've been popular during the peak of
the interstate highway system that was

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being built in the 1950's, and in fact,
that's what you see. You see this curve

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going up and then going down. If you look
at the frequency of the word network, what

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you see is you see it goes on very low,
and then boom it takes off like this. And

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when you look at this, you might wanna say
oh, look, there's a tip. We've got a tip

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right here. Remember, no, that's probably
not the case. This is probably just a

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standard Growth process. This is probably
just a standard growth process where

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interest in networks has been growing and
growing and growing. And so what we get is

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one of these nice curves that just heads
up and up. Now wh-, where this'll end, who

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knows? Maybe we'll just become awash in
talking about networks, and that's all

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we'll talk about. But at some point, it'll
probably level off, with, with some

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reasonable level of discourse on networks,
just like we talked about other concepts.

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Okay, so why are networks so cool? Why do
people care so much about them? Why have

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they become so much part of the public
discourse? Well one reason is they're just

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so fun to look at. So here's a graph of a
middle school. The white dots are

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Caucasian students. The green dots are
African American students. And the red

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dots are students of a mixed race. What
you see when you look at this graph is

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that middle school is pretty segregated.
You also see two other little; you also

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see some little clumps within the white
students and clumps within the black

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students. Those happen to be boys and
girls so you see that wow, adolescents

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tend to segregate by race and they tend to
segregate by gender. Now you can look at

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adult friendship networks, so this is From
the Framingham, the Framingham study, A

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famous study where they asked people who
their friends are. And this just shows a

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network of friends. And what you can see
is that, there's little clusters. So

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people are, you know, people have, you
know, close cliques of friends, and

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they're connected to other people through
other friends. So you don't see that same

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sort of breaking into segments,
segregating by race and gender among

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adults that you see among adolescents. And
you can also look at email networks.

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Within a corporation, you can see, here's
a person right here who tends to email a

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lot of other people. And again by looking
at these e-mail networks you can look at

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how information flows within the
organization, figure out who is important

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to the organization, who's that
information passing from that person to

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other people. You can also use networks to
look at, as I mentioned, polarization in

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American society. So this is a network
from one of my colleagues, Lada Odamick,

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and what she does, which is very
interesting, is she paints the liberal

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bloggers blue, and red blog, and
conservative bloggers red, and then she

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draws links between. Liberal bloggers as
blue lines and links between conservative

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bloggers as red lines, And the handful of
liberal to conservative links so this is

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as if a liberal blogger cites a
conservative blogger, she makes that

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yellow. And if a conservative blogger
links to a liberal blogger, she colors

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that purple. So if you look at this graph,
there's lots of blue lines, lots of red

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lines, very few Yellow and purple lines.
So, what this tells us is that discourse

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on issues is very poloroid. Now there's
something that we might think that by

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writing a network that we can even see
exactly how much there is. Now by doing

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statistics on the network and possibly
doing that over time, we can see whether

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that trend is increasing or decreasing.
Now you can also do some pretty fabulous

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stuff this is some work by Dan Katz And
his colleagues. He was, well, a student of

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mine actually at the University of
Michigan. Now he's a law professor at

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Michigan State. I think he's taking this
class, hi Dan, and one of the things Dan

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did was he looked at this set of ideas
within legal journals and then he codes

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the ideas by the schools which they
belong. So what you see is you see schools

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like Harvard, Berkley, Yale, Michigan,
NYU, Columbia in the center of this graph

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and also being bigger nodes. And what
you've got there is you've got lots of

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people are connected. Lots of ideas are
connected to those nodes. So what are we

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going to do in this set of lectures? We're
really going to focus on three things.

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First we're going to focus on the logic of
networks. How did they come to be? What

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rules do people or organizations use to
form connections to other people and

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organizations? Second, we're gonna talk
about the structure. Once you've got a

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network, you can ask, what is the, what
are the measures? You know, how do we, how

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do we compare one network to another? So
what, what are the properties of network?

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How many nodes are there, how many edges
are there? How connected are they? That

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sort of stuff. Third thing we're gonna do
is we're gonna talk about the

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functionality of the networks. So when you
think of the network, it's got some

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structure to it. We can ask, what does
that structure do? So, for example, when

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people talk about social networks, one
thing they'll talk about is six degrees of

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separation. In fact, you can get from any
one person to any other person through six

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connections. That's a functionality of the
network. But what's interesting about that

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functionality is, no one set out to form a
network that [inaudible] did that. That

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just emerges through the process. So,
here's what you want to think about,

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there's a logic to which the network
forms. That creates a structure, and then

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that structure has emergent
functionalities such as the six degrees

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property. So, that's how we wanna frame
this entire discussion. Logic is how it

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forms. Structure is the measures, you
know, in how connected are things. How far

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is it to one person to another? That sort
of thing, And then Function is what that

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structure enables the network to do. And
often, what that structure enables that

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network to do isn't something that anybody
set out to have the network do. So, it's

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an emergent functionality. However, when
we study this, we're gonna have to do this

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in a slightly different order. We're gonna
start out by looking at structure. The

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reason we're gonna do that is we need to
be able to define what a network is. What

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a node is, what an edge is, and just
describe networks before we can really

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talk about how they form. So, we're gonna
switch the order a little bit but we're

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gonna start up with structure, then we'll
gonna move on to logic, talk about how

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they form. And then we'll conclude by
talking about their functionality. Now

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this is a very introductory set of Notes
and thoughts on networks. One of my

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colleagues, Mark Newman, is [inaudible] a
book on networks that sort of starts very

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simple then moves you fairly quickly to
the frontiers of network theory. So I'd

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encourage you to pick up this book by mark
or possibly any other book on networks if

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you really want to do a deeper dive. So
this is just really a very thin

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introduction to what has become a deep,
deep area of research where there's lots

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of interesting results. I'm just going to
give you a hint of those in this set of

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lectures. Okay, so let's get started. This
is going to be a lot of fun. We're going

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to talk about the structure and the logic,
and then the function of networks. Thanks.