So you can ask yourselves the same question again. Is that enough? Is that going to always give us one unique consensus or one unique ranking of web pages? And the answer now is yes, we do have enough and that will always guarantee that we will have a unique solution with that page rank algorithm. And taking those two things into consideration does give us the page rank scheme. And so as the process we presented before, which accounts for dangling nodes and disconnected graphs that forms the basis for our page ranking. As with any company, you can assume that they are using a slightly different approach and they optimize it a lot over time. But that's the basic idea of how they go about ranking the web pages. Notice how difficult their problem is though because there's billions and billions of those web pages. So they have to be able to do the computation very quickly. And they have to, basically, deal with lots of large data sets and large data objects like matrices. And they have to be able to do computations on them very quickly, and update those computations quick. So if we take this graph again, just for a second. And just to illustrate exactly how that calculation would go with page rank. The first thing we notice again, is that V is a dangling node down here. So what we would do is we would assume there's a link coming up here. That there's a link here. There's a link to this guy, and there's a link to x. And that there's also a soft node to V. And initially then, this node disconnected components here but if there was one disconnecting component, maybe would could assume that there's nodes over here like A and B, for instance. And if they're connected to each other, going back and forth, then that other randomization aspect would basically connect them and have a pseudo connection to each of the other guys, by that randomization. Say that there is a way to get there. But it's just you have to go through your browser or the random server has to go through this browser to get there in our analogy. And we could do this for every leg. So then every node has, in a sense, a connection to every other node, as we said. So as long as we account for dangling nodes and disconnected graphs, then we can be guaranteed that that procedure will have a unique solution. So now the question is, how much randomization should we have? So in that random serving philosophy, how many times should we be just following the web graph itself versus how many times should we be jumping to random pages? Including that we'll have an affect on the algorithm itself and how quickly it can approach its solution. PageRank itself assumes a 15% randomization. And so that's basically what that's saying is that 15% of the time we're going to rely on the randomness, or just random URL's that we searched through when we used page track process. And the other 85% of the time, we're going to rely on the connectivity in the web graph. And there's a trade off there computationally in terms of how quickly the algorithm will converge. Much like what we looked at, this is a good review of the stuff with distributed power control back in the first chapter. So this is a trade off of how quickly the algorithm will converge with how much randomization we're putting in the solution. And so again, what this means is that we're following the web graph 85% of the time and we're entering a random URL 15% of the time in our random surfing analogy.