[MUSIC] I give you one more and there are several others, but the three most popular are these ones and that is the betweenness centrality and that's an interesting question. So degree centrality is how many connections do you have, closeness, how close you are. And in between is, is how often does this node lie on the path that's connecting every node with every node. The path, right? So that's what a path is and these are have a very important role, because they are gatekeepers, intermediaries, brokers on average. Because we have on average, we have to pass through this node more often. So they have a very important role nodes with the high betweenness centrality, that's actually the technical term. Your spell checker won't know, but it is correct, betweenness and that's how you write it and then it makes sense. It's the nodes that are between. So let's count that as well since we're already in that and since it's the last thing we want to go through for today has covered is the sum of the shortest path through a note or shortest path, so we have no number one. So how often do I have to go through node number one? If I want to come from the left three nodes to go to all the other ones. Well, on top, the top, the top, left node has to go, well, one time through the one to go to the two. Another time through the one to go to the three and then a second [INAUDIBLE] third, four, five times to go to the upper three, right? Six, seven, eight times to go to the lower three and then it also has to go to these other bodies over here, right? So these are these two bodies on the left-hand side. It also has to go through an order number one. So it's nine, ten. So it has to go this upper node has to go ten times through node number one in order to reach all the other nodes in the network. The same happens to the other two nodes on the left side, right, to the middle left node and the down left node also has to go ten times through node number one. If you don't believe me, please do the exercise encountered for yourself just to go through node number one, ten times in order to reach all other nodes. So now it has three, three nodes, the three nodes, but I have to go ten times through node number one. So in total, I get 30 times I have to go to node number 1 just from this left hand the 3 nodes. Node number one in order to get to y, that's again, node number one had doesn't have to go to node number one to go anywhere, and. Node number two has to go through node number one three times, when? When are these returns it has to go through node number one? Well, the three times it wants to reach the left the left three nodes, right, and it has to go through node number one. So yes, three times. If it goes to these other nodes, if two wants to go to three and so forth. It doesn't have to go through node number 1. Node number three has to go through node number one, how often in order to reach certain nodes? Also, three times. In order to reach number two, it doesn't have to go through number one. But in order to again, to reach the three left and no, right, it needs to know it needs to go through no number one. So also three, then the right six nodes, we just put them all together make it a little little simpler in order to go through node number one. Kind of like the same spiel, right, in order of each one of these right six months in order has to go through node number one if it wants to reach this three left ones, right? So there are six nodes on this right and cluster on the right-hand side, and each one of them has to go three times through. So okay, so now we have these numbers. 30, we have on the left side and we have plus 3 plus 3. That's 36 plus 18. Somebody has a calculator handy? 54, good. You still with me? So 54 times, we have to go through node number 1 if you want to reach from every node to every other node. All right, let's do the same for note number two. We're going to walk you through a quite quickly enjoy the show. So if I go from the left three nodes, I have to go through it seven times, because there's seven notes on the other side of the note number two. Then also for node number one, it's kind of like in the same condition as these left area to go seven times through the node number two. Number two to choose nothing. Then from node number three the other way around, I go four times through node number two. That's the left three plus plus the node number one. All right, good. And the right three nodes, also four times. Same idea, they're not the right six nodes actually. Because the upper and the lower and the same condition, they're the same condition as the node number three, right? They have to go four times through it. So here we get 56. So we have to go to node number 256 times. So they between us in reality of node number two is higher. They know number one in order to go from every note every note. I have to go more often through node number two. All right, so number two is as a critical role here on the path between between all the nodes. All right, let's test no number three, please again. Do it for yourself what we just did. Feel free to rewatch it if you're not absolutely sure what we just did and please map out at node number three. How often you have to go through node number three in order to reach from every node to every other node? So good that you're still with me then and that's just counting. There's no higher math or something involved. The good news is that if you do computational network analysis, you will use computers to count that. So you won't have to count it by hand, but it's important to do that. Ones for you to understand what it actually means. That's a very important concept between this and how often is a node between the path of other nodes. Okay, so no number three. I hope you got that, 3 times 6 plus 6 plus 6 plus nothing from node number 3 to node number 3 is nothing. And then 6 times 8., that gives you 78. So number three has by far the highest between it centrality. That basically comes from the fact that if you have the upper three nodes, right, the upper three nodes in order to go to the lower three nodes, it also has to go through number three. So there, you get a big intermeding function. So node number three mediates the upper and the lower three nodes. So then it gets this intermediation power from. So number three has the highest between this centrality is the biggest bottleneck gatekeeper in the mediary broker on average that we have in this network among these three nodes. Node number one, number two, number three. So now we saw that actually no number two which intuitively they knew we thought like well, yeah, that's in the center. According to these three centrality metrics, this is not in the center, right? It has not been in the center. It's not the most popular. It's not degree centrality. It's not the closest to everybody else. It's the closest internality and it's not the one that lies most frequently on the path between or others potentially blocking it.