Hi again. It's Matt. And, we're back now looking at a couple of examples, and talking a little bit about the challenges of modeling and analyzing networks. And, why there's actually something interesting in the course to talk about. So, in terms of outline, the part where we're basically in the first part of the course. So we're looking at background and fundamentals, definitions, and characteristics. And what I'm going to do is start with a couple of examples and the idea here is, is to give you some idea of feeling for data. view of applications and previewing the kinds of questions we're looking at and, you know, the word network is a very broad one. It covers a lot of different possible applications. And the kinds of things that we're really going to be looking at are ones where we have some sort of decision making. People are, are going to tend to be the nodes, so things like phone networks, e-mail networks marriages friendships, co-authorships, collaborations. Different kinds of relationships between different individuals. And often, we'll be taking the nodes as single people making the decisions, but often, sometimes will look at organizations and other kinds of things, so maybe countries or firms and, and so forth. So, just to fix ideas let me start with an example that comes out of paper by Padgett and Ansell, which is based on data that was originally collected by Kent. Here, what I'll do in terms of references is I'll standardly just give you the names of the authors in, in a year. And there'll be bibliographic information that you can find which full bibliography of the course which will have a list of the places where you can find every thing that I refer to in the course. And so, here, [COUGH] what they were looking at is inner relationships between the 16 major families in Florence in the 1430s. So, this was Renaissance Italy, and these different families in this particular picture that you're looking at are a tie between two families here is indicating that there is a marriage between two families. So you know, for instance, this tie right here is a marriage between the Ridolfis and the Medici. And, the important aspect of what's going on in this picture is that there are a series of different families. The period before 1430s was one where there was basically an oligarchy. So, there were many different families that were powerful, and at this point in time, the Medici rose to power. And in particular, the numbers here that we're going to talk about later in the course are indicating how central these different families are, in terms of how many paths between other families in a network paths between a given family. So for instance, if the Ridolfis and Salviatis want to get together in this network, they have to pass through Medici. The Medici lie on a path the shortest path between the Ridolfis and the Salviatis. So, in this particular situation, what is the, the 52 percent indicate? It indicates that when you look at two families in the network and you look at a shortest path between them, 52% of the time, when you're looking at different shortest paths, the Medici lie between them. That gives you an idea that the Medici were in some sense very central here and the Medici rose to power. They became the ruling family, essentially, of Florence during this time period. there's a lot of analysis in, in Padgett and Ansell's paper that you can read about. But the basic idea from looking at the network analysis is understanding that they were more central, gives us an idea of why they might have rose to power, even though, they were not the, the wealthiest at that time or most politically connected in that time period. So, we're, we're dealing with this situation where there is a network which helps us understand what was going on socially. the next slide here, situations where we have countries as the nodes instead of individuals. So these are European countries. we've got Germany, France, Greece, Italy, Portugal, and Spain. So six of the major countries in, in Europe. And in particular, now, we've got a weighted and directed network indicating how much of a country's debt, national debt, sovereign debt is held by entities inside another country. So, for instance 18% of French national debt is held in Germany. 13% of German's debt is held in France by entities in France. what does this network do for us, it helps us understand how shocks in one country can propagate to affect another. So when we look at some of our models of contagion and diffusion and so forth, what we'll do is we'll analyze networks, which will be very helpful in analyzing how this works. So this is from a recent paper I've been doing with Matt Elliott and Ben Golub, in understanding the transmission of financial shocks and crisis in one country and how they might lead to devaluation or, or problems in another country. So it's some sort of transmission of, of financial stress. So these are two examples that give us an idea of things that are illuminated by looking at network data and the kinds of things that we will be studying in the course that are going to take advantage of building models of networks that we can understand these interactions. And what we know about networks is that they're critical in many settings, job context, crime, risk sharing, trade and politics. there's a risk sociology literature which shows that network structure does impact behavior. and as we just saw, the Medicis were not necessarily the wealthiest or the strongest politically, but they were the most central in a well-defined sense. And one of the things we're going to start with here, is that there will be something systematic we can say about networks. And in particular when we, you know, start thinking about the importance of networks, the fact that these specific relationships are going to matter, means that we have to be able to talk about what's the shape of a network? Can we say something systematic aboutum, how networks are shaped and how the shape transmits into behavior? so what do we know about networks? We know many things. and in particular, networks are important in a variety of different settings, from how people hear about jobs finding information about employment to crime, to risk sharing. So if I have a problem, and I'm out, out of work for a while, can I borrow money from friends? Can I get help from friends? how does trade occur? understanding political alliances and behavior and, and legislature is a whole series of things. And there's a very rich sociology literature, which makes clear how some of these things matter. And as we just saw, the Medicis were not necessarily the wealthiest or strongest, but looking at networks can help us understand something about why they might have been able to take advantage of positions to advance themselves. understanding characteristics in networks can be very important, so we'll be looking at things like the path links and local properties of networks small worlds, what's known as small-worlds degree-distributions. So how, how skewed is a network? Are there people who have lots of connections and other people who have few? Or, does everybody typically have the same number of connections? Those kinds of things are going to matter. Now, in understanding things, it's going to be important that we embed, whatever the behaviors are inside a network. So, whether, if want to to understand how markets work, we'll have to understand something about what the, the different links represent in a network. so, specific relationship are going to matter, how do they matter, what's the process by which people make trades, and so forth? just in terms of, of giving basic motivation and background, one thing we can say is that, there are a number of settings that we know networks play an important role. In one of the classic areas that have been studied quite extensively is the role of networks in labor markets. In particular, how people end up finding out about jobs. So some of the early work in this area, Myers and Shultz looked at they, what they did is they surveyed a series of textile workers in the late 1940s. So, the paper was published in 1951. And what they found was that you know, asking people how did you find out about your job? Actually, 62% found out about their first job in, in the textile industry from somebody already there. So they had a contact who was in the textile industry that was what got them in there. Only 23% in contrast found by, their, their job just by applying directly 15% by agencies and ads and so forth. So you can see that the, the actual network of contacts was a very important player in how people were finding out about jobs in the textile industry. later studies Rees and Schultz, for instance, 1970, is another classic. What they did is they went around and interviewed people in different areas different professions, and they found that it wasn't simply textile workers that were finding their jobs through contact networks. typists don't really exist anymore, but at the time if you wanted something typed up, you had a typist. 37% of those people were finding their job through, through contacts accountants 23.5, material handlers 73.8, janitors 65, electricians 57. So there was a range, you know, ranging from 20 to 80%, roughly. But, overall word of miles and being connected with individuals was an important way of finding jobs, no matter what profession it were in. There's been a whole series of other studies, Granovetter's work on this is, is quite influential. there's a nice survey of this literature by Ioannides and Loury in 2004. And when we begin to look at, at this, it's not just that networks are important in labor markets, but we see that networks have played a role in a, a series of other settings as well. So just to mention a few, to keep this in our, in our minds as we go through the course. networks have been looked at in, in criminal settings. So 2 3rds of criminals actually commit crimes together with others, so that they're not acting alone. theres' evidence that social interactions play important it, it rolls in determining who be, becomes a criminal in a youth and has delinquency rates. in markets there's a whole series of of studies that have looked at things like how people make contacts, business contacts, who you end up working with, who you end up contracting with. Brian Uzzi has a nice paper looking at you know, how the importance of, of specific contracts in the garment industry. So, who ends up producing a garment for which designer. there are things like you know repeated interactions and, and fish markets can can be represented in network structures, social insurance, risk sharing. when we look at the fusions, they're going to be important roles here, so understanding which farmers end up taking up hybrid corn, at which point in time, which doctors end up prescribing different drugs at different time. So it'd be a whole series of different things and, and the, the range here is going to be quite extraordinary. Okay, so the main challenge we're going to face in the course is the complexity of networks. And what do I mean by the complexity? So let's do a very simple calculation. So, imagine you have just 30 nodes, so a fairly small society. 30 individuals, say a classroom in a, in a, a school. and we ask how many different possible networks could there exist that represent the friendships in that classroom. Well, it could be that it’s an empty network, nobody’s friends with anybody. It could be that it’s a complete network, everybody’s friends with everybody else. the number of possible networks in that classroom is actually enormously large. So person one could have 29 different friendships, right? They could be friends with person two, three, four, five, what, up to 30. person two could have 28 friendships, not counting person one, and so forth. So if we ask how many, what are the number of different friendships that could be either present or not present in that classroom? When you total all those numbers up, that's 435 in total. So that's 30 choose 2 in, in terms of the combinatorics. 435 different possible friendships, of pairs of individuals who could be friends with each other. So that's 435 possible links that could be either present or not. And when we look at 435, friendships, we've got 2 to the 435 possible networks that could be there. So each one of those links could either be present or not. 2 to the 435. Well, 435 doesn't sound like that big a number. But 2 raised to the 435th power is an enormous number. So, the estimates of, of how many atoms in the universe there are, somewhere between 2 to the 158th and 2 to the 246th. So, if we look just at one network in one classroom, we've got more possible networks than there are atoms in the universe by, by orders of magnitude. So, there's no possible way that we can just describe networks by saying, you know, it's, it's network number 53. we're going to have to find ways of describing these networks that are going to [UNKNOWN] capture the basic properties of the network in a very succinct and, and simple way. So that we don't have to, to just go a giant catalogue of, of different possible set networks that are out there. It's simply overwhelming. So that, the main part of the challenge that we're going to have to deal with first is just representing networks and thinking about, how do we capture this complexity in a way that makes sense. And so that's going to be the beginning of, of, of our definitions, how do we represent networks, how do we capture them?
