So let's return to our first example to calculate what the clustering coefficient is for this, because we already saw that the average shortest path distance was 1.4. So, first thing we want to do is count count the number of triangles that we have here. And so we see very quickly and easily that ABC is one triangle. CDE is another triangle, which is just two triangles. And then you can look throughout the rest of the graph and there's going to be no set of three nodes that are connected in a triangle such that each node can get to each other one exactly one hop. So the number of triangles that we have is two. So the number of triples that we have, well, from each of these triangles. We know that we already have three connected triples. So that's going to be 2 times 3, which is 6. But then we have other ones that we need to account for, as well. First we, we can go from, we have ACE, on the top here. ACE is another one. So it's plus 1. We have ACD, which is another 1, plus 1. We have BCE, that's another 1. And we have, also BCD, which is another 1. That's going to be ten triples. So let me just write down what those triples are here. In addition to the triangles, we have A, C, D as a triple. We have A, C, E. We have B, C, E and we have B, C, D. So, that's how we get ten triples. So now the clustering coefficient, as we said is going to be the number of triangles divided by the number of triples over 3. So we have 2 divided by 10 over 3 which is going to be equal to 6 over 10 which is 0.6. Actually the same as the clustering coefficient that we had in the other example. Now for a random graph let's see, we're going to try and do a random graph and see what the clustering coefficient is in that case. So, the clustering, the general formula for clustering coefficient of a random graph is the average degree of a node. And we take the average degree at which, the degree of a node is just the number of connections it has, remember that. And we divide that by the number of nodes minus 1. >> Okay. >> So, without going to mathematical detail, this, this should make sense right because as the average degree of a node increases ther's going to be more of a chance of forming triangles, obviously, because the node's going to have more of a chance of connecting two people who already know each other. And in the extreme case that every node is connected to every other node then the average degree of a node is just going to be the number of nodes minus 1 because the node can't connect to itself, which would give us a clustering coefficient of 1. So in the extreme case as we have said, this would approach 1 also. So let's consider example of Facebook really quick. [SOUND] So let's consider the example of Facebook and see if we have the same number of nodes we have in Facebook and the number of friends that we would typically have in Facebook, what would the clustering coefficient be if Facebook was a random graph? So Facebook is not a random graph, but assume for a second that the generation model for Facebook was a random graph. So, in the case of Facebook we have about 1 billion nodes, say. So that's about 1 billion people, at least at the time of this lecture was created on Facebook. And say every person on average has about 300 friends. So then for Facebook the clustering coefficient would be 300 which is the average degree of the nodefin. And we divide that by roughly 1 billion, so it's 1 times 10 to the ninth. Which is 3 times 10 to the negative seventh, which is really small number. So we have six zeros, 3, 4, 5, 4, 6 followed by a 3. So it's just an extremely, extremely, small number, just way too small. For a realistic social network. So, the clustering coefficient for a random graph cannot explain what we would expect to see in a social network. Therefore, the random graph is not going to be a good model to be able to explain small world.