3.12: Week 3 Wrap

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From the course by Stanford University

Social and Economic Networks: Models and Analysis

415 ratings

Stanford University

Social and Economic Networks: Models and Analysis

415 ratings

Learn how to model social and economic networks and their impact on human behavior. How do networks form, why do they exhibit certain patterns, and how does their structure impact diffusion, learning, and other behaviors? We will bring together models and techniques from economics, sociology, math, physics, statistics and computer science to answer these questions. The course begins with some empirical background on social and economic networks, and an overview of concepts used to describe and measure networks. Next, we will cover a set of models of how networks form, including random network models as well as strategic formation models, and some hybrids. We will then discuss a series of models of how networks impact behavior, including contagion, diffusion, learning, and peer influences. You can find a more detailed syllabus here: http://web.stanford.edu/~jacksonm/Networks-Online-Syllabus.pdf You can find a short introductory videao here: http://web.stanford.edu/~jacksonm/Intro_Networks.mp4

From the lesson

Random Networks

Poisson Random Networks, Exponential Random Graph Models, Growing Random Networks, Preferential Attachment and Power Laws, Hybrid models of Network Formation.

3.1: Growing Random Networks17:42

3.2: Mean Field Approximations 8:12

3.3: Preferential Attachment 10:56

3.4: Hybrid Models 14:45

3.5: Fitting Hybrid Models 17:05

3.6: Block Models 9:37

3.7: ERGMs 9:05

3.8: Estimating ERGMs 15:58

3.9: SERGMs 9:43

3.10: SUGMs 6:00

3.11: Estimating SUGMs (Optional/Advanced 21:03)21:05

3.12: Week 3 Wrap3:16

Meet the Instructors

Matthew O. Jackson
Professor
Economics

Well folks, so let's take a quick look back at what we've learned in this weeks

lectures. So, in terms of growing random networks,

what we saw was beyond just providing a realism in terms of different nodes being

born at different times. What they did was provide a heterogeneity

based on age which allowed older nodes to have higher degrees.

Younger nodes to have relatively lower degrees.

And so it gave us an increased difference in the degrees of different nodes.

So it started to give us fat tails and, in particular, if we went all the way to

the extreme of preferential attachment. Where we now add in the fact that when a

node is born it wants to connect to better connected nodes.

Then we got extreme versions of fat tails, Power laws, and that begins to

give us an idea of why we might be seeing.

Or how we might end up with very fat tails in a degree distribution.

Now, many networks empirically lie between two extremes, so we looked at

some models. That allow people when they're forming

links to form some uniformly at random. And then some by searching neighborhoods

of those nodes, and finding and needing new people.

Connecting to them, and through this combination process we end up with

something which is in between, and spans in between.

And relatively depending on how much randomness there is, in terms of uniform

and how much is, is done through searching the network.

We end up with whole series of different degree distributions which allow us to

begin to fit different models. So this, this hybrid aspect allows us

then to do then to do some estimation and see what might be going on.

And we see that, you know, some networks are formed more by searching, and others

not. And, and this is quite natural if you've

ever done a bibliography search, for instance, if you're searching for

references? You might poke around and, and randomly

come across things. But then you also when you find an

article that seems to be relevant, you'll search through its reference list to find

other articles. And so finding the ones that it cited,

can be very useful. And so that would be one explanation for

why you tend to see fat tables in, in citation networks.

looking beyond just the fact that you, things that are better cited are easier

to find. They're in fact easier to find through

other articles that you're citing and, and that process then leads also to

things like clustering and so forth. Last thing we talked about was a, another

class of, of models for doing statistical estimation.

Exponential Random Graph models. They're flexible, they capture a lot of

different things. We saw that they have challenges in

estimation. And in particular, the, calculating the

relative probabilities is difficult by the sheer number of networks that can be

out there. And so there's new techniques.

There's variations on these models where instead we work directly in a statistics

base. And those things can actually be

estimated fairly quickly. And there will be new software coming

out. And we'll possibly take a look at those

in our exercises. So what we've done is gotten some feeling

for the different random Network models. The ones that are out there, how they

explain different things. And now what we're going to be doing

going forward is, is next looking at Strategic models and then eventually

looking at behavior.

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