Hi. In this set of lectures, we're gonna
talk about networks. Networks have become
an incredibly popular topic for a variety
of reasons. One is, the internet has
allowed us to make all sorts of network
connections with people, and to give us
graphs of those networks. We're just more
aware that networks exist. Another thing
is that we get more and more data on
networks. We're getting to see the
importance of networks for all sorts of
things, Whether it's scientific
innovation, whether it's the spread of
ideas, Whether it's the polarization of
critical thought, And whether it's the
rise of. With a decrease in smoking with a
rise in social trends, You can see these
effects through networks using new
techniques. What we want to do in this set
of lectures is understand a little bit
about how networks work and why they're so
important. So first thing I just want to
convince you the networks have become a
hot topic. So what I'm gonna do is I'm
gonna pull up a couple of graphs from
Google N Gram and what this does is it
looks at the frequency at which words are
used Over time. So, they basically
scanned, they've scanned in millions of
books and this tells you the frequency of
particular words. So, the first word we're
gonna look at is interstate. So, this
would've been popular during the peak of
the interstate highway system that was
being built in the 1950's, and in fact,
that's what you see. You see this curve
going up and then going down. If you look
at the frequency of the word network, what
you see is you see it goes on very low,
and then boom it takes off like this. And
when you look at this, you might wanna say
oh, look, there's a tip. We've got a tip
right here. Remember, no, that's probably
not the case. This is probably just a
standard Growth process. This is probably
just a standard growth process where
interest in networks has been growing and
growing and growing. And so what we get is
one of these nice curves that just heads
up and up. Now wh-, where this'll end, who
knows? Maybe we'll just become awash in
talking about networks, and that's all
we'll talk about. But at some point, it'll
probably level off, with, with some
reasonable level of discourse on networks,
just like we talked about other concepts.
Okay, so why are networks so cool? Why do
people care so much about them? Why have
they become so much part of the public
discourse? Well one reason is they're just
so fun to look at. So here's a graph of a
middle school. The white dots are
Caucasian students. The green dots are
African American students. And the red
dots are students of a mixed race. What
you see when you look at this graph is
that middle school is pretty segregated.
You also see two other little; you also
see some little clumps within the white
students and clumps within the black
students. Those happen to be boys and
girls so you see that wow, adolescents
tend to segregate by race and they tend to
segregate by gender. Now you can look at
adult friendship networks, so this is From
the Framingham, the Framingham study, A
famous study where they asked people who
their friends are. And this just shows a
network of friends. And what you can see
is that, there's little clusters. So
people are, you know, people have, you
know, close cliques of friends, and
they're connected to other people through
other friends. So you don't see that same
sort of breaking into segments,
segregating by race and gender among
adults that you see among adolescents. And
you can also look at email networks.
Within a corporation, you can see, here's
a person right here who tends to email a
lot of other people. And again by looking
at these e-mail networks you can look at
how information flows within the
organization, figure out who is important
to the organization, who's that
information passing from that person to
other people. You can also use networks to
look at, as I mentioned, polarization in
American society. So this is a network
from one of my colleagues, Lada Odamick,
and what she does, which is very
interesting, is she paints the liberal
bloggers blue, and red blog, and
conservative bloggers red, and then she
draws links between. Liberal bloggers as
blue lines and links between conservative
bloggers as red lines, And the handful of
liberal to conservative links so this is
as if a liberal blogger cites a
conservative blogger, she makes that
yellow. And if a conservative blogger
links to a liberal blogger, she colors
that purple. So if you look at this graph,
there's lots of blue lines, lots of red
lines, very few Yellow and purple lines.
So, what this tells us is that discourse
on issues is very poloroid. Now there's
something that we might think that by
writing a network that we can even see
exactly how much there is. Now by doing
statistics on the network and possibly
doing that over time, we can see whether
that trend is increasing or decreasing.
Now you can also do some pretty fabulous
stuff this is some work by Dan Katz And
his colleagues. He was, well, a student of
mine actually at the University of
Michigan. Now he's a law professor at
Michigan State. I think he's taking this
class, hi Dan, and one of the things Dan
did was he looked at this set of ideas
within legal journals and then he codes
the ideas by the schools which they
belong. So what you see is you see schools
like Harvard, Berkley, Yale, Michigan,
NYU, Columbia in the center of this graph
and also being bigger nodes. And what
you've got there is you've got lots of
people are connected. Lots of ideas are
connected to those nodes. So what are we
going to do in this set of lectures? We're
really going to focus on three things.
First we're going to focus on the logic of
networks. How did they come to be? What
rules do people or organizations use to
form connections to other people and
organizations? Second, we're gonna talk
about the structure. Once you've got a
network, you can ask, what is the, what
are the measures? You know, how do we, how
do we compare one network to another? So
what, what are the properties of network?
How many nodes are there, how many edges
are there? How connected are they? That
sort of stuff. Third thing we're gonna do
is we're gonna talk about the
functionality of the networks. So when you
think of the network, it's got some
structure to it. We can ask, what does
that structure do? So, for example, when
people talk about social networks, one
thing they'll talk about is six degrees of
separation. In fact, you can get from any
one person to any other person through six
connections. That's a functionality of the
network. But what's interesting about that
functionality is, no one set out to form a
network that [inaudible] did that. That
just emerges through the process. So,
here's what you want to think about,
there's a logic to which the network
forms. That creates a structure, and then
that structure has emergent
functionalities such as the six degrees
property. So, that's how we wanna frame
this entire discussion. Logic is how it
forms. Structure is the measures, you
know, in how connected are things. How far
is it to one person to another? That sort
of thing, And then Function is what that
structure enables the network to do. And
often, what that structure enables that
network to do isn't something that anybody
set out to have the network do. So, it's
an emergent functionality. However, when
we study this, we're gonna have to do this
in a slightly different order. We're gonna
start out by looking at structure. The
reason we're gonna do that is we need to
be able to define what a network is. What
a node is, what an edge is, and just
describe networks before we can really
talk about how they form. So, we're gonna
switch the order a little bit but we're
gonna start up with structure, then we'll
gonna move on to logic, talk about how
they form. And then we'll conclude by
talking about their functionality. Now
this is a very introductory set of Notes
and thoughts on networks. One of my
colleagues, Mark Newman, is [inaudible] a
book on networks that sort of starts very
simple then moves you fairly quickly to
the frontiers of network theory. So I'd
encourage you to pick up this book by mark
or possibly any other book on networks if
you really want to do a deeper dive. So
this is just really a very thin
introduction to what has become a deep,
deep area of research where there's lots
of interesting results. I'm just going to
give you a hint of those in this set of
lectures. Okay, so let's get started. This
is going to be a lot of fun. We're going
to talk about the structure and the logic,
and then the function of networks. Thanks.