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.