central focus in this course is really going to be on the models and the types
of, of techniques we'll be using are one, pulled from random graph theory, pulled
from mathematics. The other, we'll be using some strategic
and game theoretic techniques, and we'll also be using some hybrid models that
involve some, both choice and chance. And looking at some statistical models
for fitting and analyzing networks, dealing with data.
goals, I'm not going to presume, prior knowledge of network analysis.
I'm going to try to introduce you to variety of different approaches, so the
idea here is really breadth, more than depth, so its an idea of giving you, some
exposure, so you know what's out there. The types of different tools, which tools
might be appropriate in different settings.
There's a lot more that can be said about each of the subjects we're going to talk
about, but this will be more or less an introduction, to give you an idea of
exactly what the tools are that might be appropriate for different parts of
analysis. It'll also give you some sense of
different disciplines' techniques and, what the kinds of questions and
perspectives that they take. In terms of, one important aspect when I
start the course here is, is really emphasis.
Why do we care about modelling things to begin with?
And I think this is an important question that, that will shape the structure of,
of what kinds of models we work with and, and how they're formed.
And, you know, when we look at models, one thing they do for us is give us
perspective into why we see certain things.
So why do social networks have short average path lengths for instance.
Why is it that there's six degrees of seperation in the world.
Well, we'll see an answer to that, that will come out of random graph model.
So, just understanding the structure of how things arise at random, can help us
understand why we might see something like that.
So understanding a basic tree structure that underlies social networks, will help
us understand path length. models also about to compare the
statistics. So if we understand that models changfe
as we change different parameters, that can help us make predictions about how
the world might change. So, how, how does the component structure
change with density. If a, if a network has more and more
links, what does that do to the overall component structure of the network.
It will help us make predictions out of samples, so if you want us to come in
with a new policy for instance you are trying to, to stamp out a flu, epidemic.
how effective does the vaccine have to be in order to, to limit, the extent of a,
the epidemic. That's a question we can begin to answer
with network analysis. things will also the models will allow
for statistical estimation. So, if we wana understand, for instance,
is their significant clustering which means, you know, are my friends friends
with each other. does that happen, because of some social
force, or is it happening just at random? we can test models.
So we can take models and, and then ask does this appear that this happened at
random, or does it appear that it something else was going on.
So there'll be statistical tests that we can use once we have models for analyzing
that kind of question. in terms of a basic outline of the
course, it's going to break into three parts.
The first part's going to be background and fundamentals.
So, definitions. How do we analyze networks?
What are some basic, properties of networks, characteristics.
And along with this will be empirical background.
The second part of the course, and the central part of the course is going to be
network formation models. So we'll look at random graph models, and
then we'll also look at strategic formation models when people are actually
making choices. the third part of the course is networks
and behavior. That's going to then take networks and
understand how the shape of networks and the structure of networks,
Who do you know, how many people do you know, who do they know and so forth.
How does that influejnce what you're dedcisions are, your behavior and so
forth. So we'll look at things like diffusion
and contagions. We'll look at learning models.
And then finally, what's known as games on network or situations where what I do
depends on the choice of my friends. So if there's a new app out there, do I
want to get it? Well it might depend on how many of my
friends get it and that might depend on how many of their friends get it, and so
forth. And so how do we analyze that in a
network context. So more or less these three main parts
are going to be the core structure of the course.
And there's a text book which is completely optional, that I've written
where a lot of the material is going to be pulled for.
In terms of this outline, the numbers on the side here indicate the chapters, so
one two, three four five and so forth, these indicate the relative chapters out
of the book that, that correspond to the lecture structure of the course.
So we'll be moving along through the book with, with a, a couple of exceptions in
terms of which chapters are covered in which part.
So that's the basic outline. And so let's get started.