[MUSIC] Triadic cencus, allows us to go one step beyond simple counts of trades in the network. Let's look at what it entails. With undirected data, there are four possible types of triads, which means we have 0, 1, 2 or or 3 relations. Accounts of the relative preference of these four types and relations across all possible triplets, which is a triad cencus. Can give a good sense of the extent to which the population is characterized by isolation when there are no connections or couples only when there are only one diet, relations in a triad clusters or structural holes. For example, when one actor is connected to two others who are not connected to each other. So that's for undirected network. With direct the data, as we know, there are 16 possible tryouts and those 16 possible tryouts, exhibit hierarchy equality and the formation of exclusive groups where two actors connect and can exclude the third. They all rely on the really fundamental forms of social relationships that can be observed. Transitive tryouts play a type of a balance away if A director type two B and B director type two C. Then A, mite natural directed tight to C, of the 16 possible types of directed tryouts. Six involved 01 or two relations and can display transitivity, because there are not enough times to do so. One type of three relations A, B, B, C, and C. B does not have any other triplets and hands can display trans activity in three more types of triads. There ordered triplets, A, B and B, C. But relations between A and C is not transitive. The remaining types of tryouts, display varying degrees of trans activity. So, we distinguish between strong trans activity and weak transitivity, but that only applies to value data. A strong transitivity is one in which there are connections A, B, B, C and A C. And the connection A C is stronger, than the minimum value of a strong type. A weak transitivity, is one in which there are connections A B, B C and A C. But the value of the A C is less than the threshold of a strong tie but greater than the threshold minimal value of a weak time. I know it sounds a little complex but we'll see how it looks like on the real life data set. Let's return one more time to structural holes, compare the two images. In the first image, we have three disconnected components and our ego, the actor we're interested in belongs to one of the components. There are few structural holds there, because there are only a few missing links. In the second picture, our ego is connecting to other disconnected components. There are two bridges that appear, but as a result also additional structural holes form. These many structural holes, allow for power information and freedom analysis that we can do for this particular network. How do we analyze Triadic Census? Well, typically we get the numbers of each type of a triad and we can then compare those numbers to a random network as you will learn in this course and later in other social network analysis courses. Random networks play a special part in our analysis, because lots of times we asked two main questions when we observe a network. Is our network random, is it possible that our a charter normal network was just formed that way by random chance? Or is it different from random networks? Which means we can use some of the theories we have talked about to explain the type formation and the human behavior. When you get the tried extensive analysis, you get the triad type, the triad census, which is how many you have of that type, the expected value and the standard deviations. The expected values of what we would get on average from a random directed graph. Those statistics are here to test the structural hypothesis that you might be, for example, interested in studying sometimes linear combinations of test instead of the entire census. But what's important as we can notice that for example, there is a very large difference for a triad 102, the triad, census is 143. We expect the value is 171. The same large differences present in the triad 021D. But for 021U, I'm not so sure, it looks like that particular triad combination may not be different from random network in its account. Here I want to introduce you to a fascinating study that allows us to understand the importance of trade expenses. This story comes from David White and his colleagues. The individual in the context, a social network approached the study of behavior and was actually referred to the behavior of Culbert. What has happened here, is that, the authors have calculated triad's using value data triads calculated based on the data that occurred tightly in time intervals in 15 seconds window. What's the data? That's a song that birds sing to each other. So in every 15 seconds increment, if bird 1 sinks to bird 2 and then bird 2 things to bird 3, then we get 111 G triad. And that's how that census was being conducted. Now, this is a distribution of triads. It's actually interesting if you notice at the scale there's 10 to the fifth power number of triads. Imagine how much time it's taken to record all of that data. However, more fascinating information comes not just from the scale, it comes from another information, 99% of triads, were formed in the following categories, 012, 102, 021U, 021D, 021C, 111D, 111U and that's it. Remaining 8 triads, occurred only in one of the time. Think about it. These are biological systems but not cognitive systems. Birds don't necessarily think of who they sing a bird to. Their behavior is based on biology. How much can we learn about human behavior, when we notice that, 0 tryouts, where we have 0 mutual, 0 symmetric and three now ties do not exist in this burg population. It might give us some idea that those 0 triads are actually human behavior. It was also important to notice that, for example, for undirected songs there were no interactions. So when birds didn't sink to someone in particular, nobody sang back. Or when there was a mail directed song, there were also no interaction. But, when there were female directed song, that's 94% of just three types of triads. There are some additional fascinating results. And you can read them in the study if you wish. We should move on to another network concepts. But I hope you find tragic analysis as interesting and exciting as I do. So, we will of course discuss tried examples in the context of our case study example, let's open our and look at what insights we can generate from our case studies. [MUSIC]