So again, we're confined to what we can write on a single page just like in the last section or the one before that when we were talking about cellular and then WiFi. You know, we couldn't do huge examples with thousands of devices because we can't write that all down on one page and we can't do all those computations by hand. But we'll, so we'll stick with something that we can look at on a page, and we'll look at this web graph over here. It's it's got four nodes, and it's got eight hyperlinks between the nodes as you can see. And we'll call the nodes W, X, Y, and Z. That'll be their names. So, the first question we have to ask is what really makes a page important, right. So, we'll try to get into Google's head here and let's see what exactly that would mean by important. So, we have to figure out amongst these web pages in terms of who's pointing to who, how we determine which one's are the most most important. So, first thing is how do we really measure that? Well, one way we could do that, a simple way, is by looking at maybe the number of links that are pointing to a node, right. So W here has one incoming link, which means there's one person referencing him. Y has three incoming links, and, and so on. That's called the in-degree which is the measure of the number of incoming links a node has, and that's a possible way of quantifying importance in-degree. there's a way we can look at it and it's a very simple way, so let's try to do that here. Try to get the in degree here. So, we said W has one incoming link form Z. So, we're just counting the number of incoming arrows. So, Ws in-degree is 1. Y has three incoming links, one from W, one from X and one from Z, so this in-degree of Y is 3. X has one incoming link. So, you see it's just one coming in from Z over here. So, this is just a one. And Z has two incoming links, one from Y and one from X, so this would be 2. So, if that's the that Google was going to quantify importance, you'd say, well, Y has the most people pointing to him. He is the most popular. And then Z has the second most, and he's the second most popular. And then, W and X each tie for 3rd. So, the output page might look something like this where we'd show Y first. Then we'd show Z second on the search result page. And then, we'd show either W or X, and that those could be interchanged, depending. So, the question is, does this tell the whole story? So, have we come up with an efficient measure to quantify importance in terms of this in-degree measure over here? Which again, is just the measure of the number of incoming links each node has. So, it turns out that Google really doesn't think so, and their algorithm doesn't use something this simple. We have to get more complicated in terms of it. And the real reason is that just intuitively, we could just point this out right now, we'll quantify it more in a minute. But we're not taking into account the quality, so to speak, of each of these links, right. So, a link coming from W might not mean as much as a link coming from Z, for instance, because as we said Z is more popular than W. So, because Z is porting to Y, that link might mean more than this link W coming to Y. So, we need to also take that into account as well, right. So, for instance, if your favorite rock star gives you a shout out or something or links to your page, that's going to create, cause a lot more people to be able to go to your page and make your page a lot more quote unquote important than if it's just one of your other friends who doesn't have that many connections as someone famous would.
