Hi folks again. So we're back again, and now we're talking still about network structure and so forth. We're going to talk a bit about what's known as homophily. And in terms of the overall outline of the course, we're still in the first part where we're talking about background and basic definitions and characteristics of networks ways of representing networks and tying this in with some empirical background which gives us some feeling for what kind of things are observed and not. And in particular today's subject is Homophily. And what this refers to is the fact that when we, instead of just looking at the network without node attributes, we actually keep track of characteristics of nodes, we tend to find that linked nodes are similar to each other. So you know, this is something that's been recognized in human interactions for millenia. And, in particular, Here's a quote by, Philemon Holland from 1600. Birds of a feather flock together. depending on your translation. Or as commonly, birds of a feather will fly together. so similar types interacting with similar types. It's been looked at across a, a variety of, of different dimensions. So age, race, gender, religion, profession, and the term Homophily itself[COUGH] was coined by Lazarsfeld and Merton in a 1954 paper. And um[COUGH] it's really been documented across many different studies so you know, studies of, of gender and ethnicity. profession and you know grade and race and schools. A whole series of different attributes. And to give you just some feeling for this, uh,[COUGH] where Peter Marsden study. I'm looking at a national survey in the US. only 8% of people actually and anybody of another race, of they, of with they would discuss important matters. and that's much lower then you would expect if, if people were just naming people with, without regards to race. So if it was balanced in terms of what the population is. interracial marriages in the US. a study by Roland Fryer /g, 1% of, of whites marry outside of white. 5% of Blacks, 14% of Asians the number is going to differ based on the size of the sub populations. Basically what you see is less than what should be expected if these things are happening uniformly at random. High School, Middle School friendship less than 10% of expected. Cross-raced friendship. Is always an interesting one, when you look at closest friends, 10% of men name a women, 32% of women name a man, so you've got some asymmetries there, but also again well below at what you should see at roughly 50% if there was not any bias in that. here's a picture from[COUGH] a high school in the[UNKNOWN] data set again. This is from work I did with[UNKNOWN] and[UNKNOWN] an what we're looking at here is a given high school and nodes are colored now by their, self reported um,[UNKNOWN] so the blue notes are blacks. The you can see there is a few red nodes, which are Hispanics, the other nodes are whites, and what you begin to notice here, this was actually drawn by what's known as a spring algorithm. And the idea of a spring algorithm is you could think of, of links like springs and imagine these springs trying to pull nodes together that are linked. So if I'm linked to a bunch of other things then those nodes would try and collapse it. So a spring algorith tries to relocate the nodes on the page. In a way where nodes that are connected to each other are pulled closer to each other, and without just collapsing everything to a giant small ball. so you, you have to keep the, the, a certain spread of the nodes on the page, and then when nodes are connected to each other, you, you try and move them closer together. And so what that does is it begins to show you that there is a separation where most of the Blacks are in, in one group, most of the Whites are in another group. here the Hispanics tend to be a little more integrated. but you see a, a strong segregation pattern. You can see that visually if you begin to look at the numbers, you also see that in terms of for instance, the whites make up 52% of the population, yet 86% of their friendships are with other whites. Blacks make up 38% of the population yet 85% of their friendship are with other blacks, so this is where you begin to see the differences between what would be happening at random and what's actually happening in the data. And here interestingly Hispanics are, are somewhat outbred in the sense that they're 5% of the population, only 2% of their friendships are with other Hispanics. smaller groups will tend to have different characteristics than larger groups. but we're we're seeing a, a, a strong segregation pattern. Now if we, what I did here is instead of just looking at people's nominations as others of friends. So in this survey you could asked, you're asked to name up to five male and five female friends and that what was pictured before. Instead we can look at what people do in terms of activities. And, here these are what are known as, I put in quotes strong friendships. So these are situations where people spent, did at least three activities with another individual in a given week. So you for instance studied together, or had lunch together, or, you know, were in a class together, or something. so now friendships are going to be stronger relationships because there's more of a, of a hurdle to be crossed. And the, the network ends up being[UNKNOWN]. And in particular here when you look at this one now you see even a stronger separation so I think there was only a few links between blacks and whites, I think you know, you can see one here, there's one here, one here. There's basically like something like 3 relationships across, so depending on how you define friendships you know here when we put in a stronger definition we see even more segregation and fewer cross group relationships than before. Now this is not something that's unique to American high schools. this is a study by Baerveldt et al looking at a Dutch high school. and here you see, again, you know, the Dutch make up 65% of the population. 79% of their friendships are with other Dutch. 5% For Moroccan's, 27% of their friendships are with other Moroccan's. So again when you look at what's on this diagonal, the diagonals are basically larger than the fractions of the population. So you're seeing people have a higher tendency to be linked to their own type than different types. Now, when we begin to think about this, it's not, there's many explanations and what we can talk more about this as the course goes along, but it's not just one possible explanation. It could be that there's opportunities, you know that, that somehow. But the way in the which the calsses are structured and the posibilities that you meet people could be biased by race and so it might be that who you contact is, is race dependent. So that there's just more a chance of meeting your own type. it could be that there's benefits in costs. so having a common, set of understandings or common culture. common language in terms of, the way that you, you think about things. could make it, different in terms of how people deal with things. There could be social pressures, that are involved. there count be social competition. There is a whole series of different theories for why you might see homophily but what's going to be important here is understanding that sometimes looking at a network, if we begin to put in characteristics, we'll begin to see that, the structure of the network is characteristic dependant. And the structure of things like homophily are going to be important in understanding, for instance, why, learning might have, might have impediments in terms of the segregated network. Or why communication might result in an idea of circulation among one group and not another group. Or, understanding when it is that contagions will end up hitting a whole population as opposed to parts of population. So understanding homophily structures, going to be important in understanding a whole series of things once we begin to understand what the structure of networks has to do with behavior. And it's interesting to understand homophily in its own right. You know, why are we seeing these patterns? What's really going on? Why, why do we see these kind of separations and segregations? So we'll get to that more of that as we go through the course.
