# Pagerank

The World Wide Web would be a World Wide Jungle if it weren’t for this algorithm. Named after Google’s co-founder Larry Page, the algorithm organizes all the worlds information (well, mostly webpages) and makes it accessible.

PageRank is one of the methods Google uses to determine a page’s relevance or importance. It is only one part of the story when it comes to the Google listing, but the other aspects are discussed elsewhere (and are ever changing) and PageRank is interesting enough to deserve a paper of its own. But how does it work?

In short PageRank is a “vote”, by all the other pages on the Web, about how important a page is. A link to a page counts as a vote of support. If there’s no link there’s no support (but it’s an abstention from voting rather than a vote against the page).

Quoting from the original Google paper, PageRank is defined like this:

We assume page A has pages T1…Tn which point to it (i.e., are citations). The parameter d is a damping factor which can be set between 0 and 1. We usually set d to 0.85. There are more details about d in the next section. Also C(A) is defined as the number of links going out of page A. The PageRank of a page A is given as follows:

PR(A) = (1-d) + d (PR(T1)/C(T1) + … + PR(Tn)/C(Tn))

Note that the PageRanks form a probability distribution over web pages, so the sum of all web pages’ PageRanks will be one.

PageRank or PR(A) can be calculated using a simple iterative algorithm, and corresponds to the principal eigenvector of the normalized link matrix of the web.