The Google Pagerank Algorithm

Toolbar PageRank
(log base 10) Real PageRank
0 0 - 10
1 10 - 100
2 100 - 1,000
3 1,000 - 10,000
4 10,000 - 100,000
5 and so on…

PR: Shorthand for PageRank: the actual, real, page rank for each page as calculated by Google. As we’ll see later this can range from 0.15 to billions.
Toolbar PR: The PageRank displayed in the Google toolbar in your browser. This ranges from 0 to 10.
Backlink: If page A links out to page B, then page B is said to have a “backlink” from page A.

That’s enough of that, let’s get back to the meat…
So what is PageRank?

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.

but that’s not too helpful so let’s break it down into sections.

1. PR(Tn) - Each page has a notion of its own self-importance. That’s “PR(T1)” for the first page in the web all the way up to “PR(Tn)” for the last page
2. C(Tn) - Each page spreads its vote out evenly amongst all of it’s outgoing links. The count, or number, of outgoing links for page 1 is “C(T1)”, “C(Tn)” for page n, and so on for all pages.
3. PR(Tn)/C(Tn) - so if our page (page A) has a backlink from page “n” the share of the vote page A will get is “PR(Tn)/C(Tn)”
4. d(… - All these fractions of votes are added together but, to stop the other pages having too much influence, this total vote is “damped down” by multiplying it by 0.85 (the factor “d”)
5. (1 - d) - The (1 – d) bit at the beginning is a bit of probability math magic so the “sum of all web pages\’ PageRanks will be one”: it adds in the bit lost by the d(…. It also means that if a page has no links to it (no backlinks) even then it will still get a small PR of 0.15 (i.e. 1 – 0.85). (Aside: the Google paper says “the sum of all pages” but they mean the “the normalised sum” – otherwise known as “the average” to you and me.