The PageRank algorithm is a great way of using collective intelligence to determine the importance of a webpage. There’s a big problem, though, which is that PageRank is difficult to apply to the web as a whole, simply because the web contains so many webpages. While just a few lines of code can be used to implement PageRank on collections of a few thousand webpages, it’s trickier to compute PageRank for larger sets of pages. The underlying problem is that the most direct way to compute the PageRank of n webpages involves inverting an n \times n matrix. Even when n is just a few thousand, this means inverting a matrix containing millions or tens of millions of floating point numbers. This is possible on a typical personal computer, but it’s hard to go much further. In this post, I describe how to compute PageRank for collections containing millions of webpages. My little laptop easily coped with two million pages, using about 650 megabytes of RAM and a few hours of computation