All right. So back from this interlude, back to our centarlity. I've walked you through these three centrality, degree centrality, closeness, betweeness, but there are other ones. There are many others that are just as reasonable and just as important. It depends on what you're looking for. One very important, one very common one is called eigenvector centrality. Eigenvector that's a concept again from linear algebra, from matrix algebra and that has to do with the friends your friends. So degree centrality for example, makes you very popular if you have a lot of connections. But then you might have a lot of connections but all your friends might be hermit. They might not have friends themselves. So what eigenvector centrality asks is are you connected to people who are popular themselves? Are your friends, do they have also a lot of friends themselves? It goes out one degree and with the eigenvector actually you can. You can go out and out and out and calculate the highest eigenvector centrality. So it's proportional to the sum of the neighbor's centrality. That's what it calculates. Google's famous page rank, that's the algorithm that ranks the pages on your search result, that's the algorithm that converted Google into this huge company that it is today uses actually eigenvector centrality. So the page rank if you search something in Google is proportional to the sum of the rank of the linked pages. It means if a page links to your page and this page nobody links to it, that doesn't give you many points. However, if a very popular page links to you, I don't know. If they New York Times or CNN or whatever would linked to your page so by the end your page would become what get more points in this page rank algorithm. I'm going to walk you through don't worry, we've done enough counting for today. There with no calculator eigenvectors centrality really use a computer. We're going to go to software soon and we can calculate these things then with a computer. Now, another of a case study here, eigenvector centrality in some cases is extremely important. For example, in the diffusion of innovation and that's one application here, one case study I want to leave you with. For example, what this group here did, around Professor Jackson from Stanford is they studied the diffusion of microfinance. So they went to 75 rural villages in India that did not have microfinance mechanisms. So they didn't have this innovation. Then the bank that had the idea to spread this innovation entered in 43 of them and started to offer microfinance. Now, you go into a new market, the idea is now so who do you offer it to? Well, you could offer it to the most popular kid. That's what's often done in marketing especially. You hire a celebrity. You hire somebody Kim Kardashian or Lionel Messi or somebody everybody knows who has a high out-degree centrality because it's a big microphone that spreads it. So you could do that. Or you can use some other betweeness maybe, closeness somebody's close to somebody or eigenvector centrality. So that was the question. What matters here or is it more the characteristics of the people that matter? Well, the first question that you then in order for a question has the first challenge that you meet is how to represent the network. That brings me back to the beginning of the lecture and that's always what you have to decide and that comes of your creativity ingenuity as a researcher that models reality. So the question with microfinance a very reasonable question is who would you borrow from? They asked this question with 13 different kinds of what's like a multiplex network. It was a multiplex network always the same people. Then they asked different questions to make different kinds of ties. For example, they asked who would you borrow money from? Well, you get this kind of network. If you ask them who would you borrow kerosene from, you get a different kind of network. Who do you go to the temple with? You get a different kind of network. Who do you ask for advice,? You get again a different kind of network. So they didn't 13 of this kind of networks and a multiplex network basically, and then started to analyze what matters in the diffusion of this innovation, and they found degree centrality is not what really matter that didn't push the innovation forward, but eigenvector centrality. Yes, that had a big effect. So if you conduct first those whose friends have also many friends, then you take advantage of this multiplier effect. They don't go to the most popular to go to the ones the agents of change that also themselves have a big circle of influence among them. That really spread the innovation the fastest. Now, there's discussion about it that doesn't apply to every case. I mean, this case is a small village in rural India. There might be other centrality measures but that's what you can get at. Once you have the tools of network analysis under your belt you can analyze and study who to contact in what case, if you do that try to spread an innovation in a social network with millions of users you might get to a different result. But these tools are now available and you can calculate and actually make a science out of that, instead of just betting on getting the biggest celebrity, spending a lot of money, and maybe, being sub-optimal in spreading your message, be it marketing, be it a political opinion or be it any other kind of technological innovation.
