Hi folks, so now we are going to talk about

models of networks that allow us to capture interdependencies.

And these are often known as exponential random graph models.

So, we went through these different forms of

models, last we talked about stochastic block models.

And now we are going to talk about the popular set

of models which are known as exponential random graph models.

And we are also going to talk about some variations

on these kinds of models, some new types of models.

Which are easier

to estimate than exponential random graph models.

And, so I'll talk to that, after we get to, to the basics.

Okay.

So first of all, a quote from Jacob Jevy Moreno and Helen Hall Jennings from 1938.

And this sort of, you know, gives us the idea that when we're looking at

situations with, we're looking at social interactions and people

are interrelated.

We're not going to be able to look at just binary relationships diads.

We're going to have to be looking at bigger configurations.

And, so that is something that is driven home by their original, quote here.

That a pertinent form of statistical treatment is one which deals with social

configurations as wholes, and not single series

of facts, more or less artificially separated

from the total picture.

And a very interesting thing here, I pulled a, a picture from Moreno in 1932.

So, actually the Moreno is also known as the father of sociometry.

He's a social psychologist, and here, he was actually mapping

out ties between individuals in different houses, in New York.

He was at, at Columbia University in 1930s.

And this was one of

the first sociograms or situations where we've actually

mapped out a network in a graphic form

of a social interactions between individuals and one

of the first ones that I know of.

Okay, so, so lets talk about this class of models.

So, the previous models we have talked about are not great

at fitting data with lots of clustering and other kinds of dependencies.

And in particular, in testing many social and economic kinds of theories,

which will give us reasons for which people might

be, interacting with each other in certain particular, forms.

And, so the idea here is that you know, the link between two

individuals i and j could depend on the presence of a friend in common.

Does, j know k and i know k as well?

That's something we want to capture.

The difficulty with this is, once we allow one link

to depend on another link, then we open a Pandora's

box, where now all the links could be inter-dependent.

So if, if i and j dependent whether they

have a friend in common and the, that friend

depends on whether they have other friends in common

and also depending on whether i and j are there.

Everything gets put back together and so

we have to specify all of the interdependencies.

And Frank and Strauss in 1986 and they started

working with a class of models which became known

as p* models and, and were most of them imported into the social networks,

literature and, and force by Wasserman and, and Pattison in the 1990s.