# PageRank Analyzed – Day 25

August 20, 2008 by Antony

PageRank a.k.a. PR is probably one of the most misunderstood aspects of SEO. People think that they have a decent comprehension of PageRank and the fundamentals behind it. Let’s start with Google’s definition of PageRank.

PageRank relies on the uniquely democratic nature of the web by using its vast link structure as an indicator of an individual page’s value. In essence, Google interprets a link from page A to page B as a vote, by page A, for page B. But, Google looks at more than the sheer volume of votes, or links a page receives; it also analyzes the page that casts the vote. Votes cast by pages that are themselves “important” weigh more heavily and help to make other pages “important.”

Important, high-quality sites receive a higher PageRank, which Google remembers each time it conducts a search. Of course, important pages mean nothing to you if they don’t match your query. So, Google combines PageRank with sophisticated text-matching techniques to find pages that are both important and relevant to your search. Google goes far beyond the number of times a term appears on a page and examines all aspects of the page’s content (and the content of the pages linking to it) to determine if it’s a good match for your query.

This is a great quote, to the point, and from the source. Obviously Google ranks and weighs their PageRank formula high as it is their foundation for search engine results and their algorithm. Consider PR like one big bowl of liquid. Each time there is a link given on a website it is like a hole is made in that bowl. Leaking out the liquid to the other websites. The more links you have the less liquid you have left and the less you can give to others. A page with high PR transfers more than a page with low PR making different PR valued links not equal in value from an SEO perspective.

**How Can I see PageRank?**

There are actually many programs created to help simplify the PageRank viewing process. Google’s toolbar, found here, will actually display a websites PR when you go to view it. Depending on your web browser I typically suggest other plug in’s then Google’s toolbar as the toolbar is bulky and a little too much. If you use Firefox install the Search Status plug-in instead. It allows for PageRank bar, Alexa bar, and many other very crucial SEO tools. found here.

**PageRank Calculations**

Remember PageRank is based upon a scale of 1 – 10, with 0 being the lowest and 10 being the highest achievable ranking. PageRank is based upon a log scale, somewhere between base 6 to 8 although we don’t know for sure as it doesn’t really matter as it is all relative. This means that each PR point increase takes 6 to 8 times the effort as the last PR increase. Here is a quick PR points table if PR is Base 8.

PR1 = 8 points

PR 2 = 64 points

PR 3 = 512 points

PR 4 = 4,096 points

PR 5 = 32,768 points

PR 6 = 262,144 points

PR 7 = 2,097,152 points

PR 8 = 16,777,216 points

PR 9 = 134,217,728 points

PR 10 = 1,073,741,824 points

As you can see the way that the PR points rank up almost exponentially rather then linearly. The higher a pages PageRank goes the even harder it is to gain the next PageRank point. Consider a point as either an incoming link from another website with a PR1. Although keep in mind a link from a higher PR means a higher point value for that link.

**PageRank Formula**

Sergey Brin and Lawrence Page, founders of Google, released their original algorithm in “The Anatomy of a Search Engine”. So let’s view what they said in order for us to better understand their anatomy of Google’s search engine.

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. Also, a PageRank for 26 million web pages can be computed in a few hours on a medium size workstation. There are many other details which are beyond the scope of this paper.

Obviously there have been changes in the algorithm over time, but this is the fundamental basis of the results for Google. The minor changes to the algorithm won’t effect the overall basis that is was built upon. So use this to your advantage, take this knowledge and understand it.

**PageRank Calculation Simplified **

The formula expressed above can be extremely confusing, especially considering that we don’t understand the countless iterations of the calculation to reach a PR value. Not to mention that since all the variables aren’t expressed we can’t accuretely predict a PR fora ny page using the original PageRank formula.

What we can do though is break it down and simplify the formula allowing for a ‘general’ idea of estimated PR transferred through a single link. This way you can understand the signifance of receiving links for higher PR websites or if you are considering to participate in a link exchange program.

Let’s replace (PR(A)) with (PR(pts)) from the PR points table expressed above (repeated below). C(A) is from the original forumula and represents the number of links found from the page in question. For those interested we also use 0.85 in the equation because it’s generally believed in the SEO community that the dampening factor in the original formula is 0.85.

PR(pts) * 0.85 / C(A) = PR points transferred via link

PR1 = 8 points

PR 2 = 64 points

PR 3 = 512 points

PR 4 = 4,096 points

PR 5 = 32,768 points

PR 6 = 262,144 points

PR 7 = 2,097,152 points

PR 8 = 16,777,216 points

PR 9 = 134,217,728 points

PR 10 = 1,073,741,824 points

**Example of PageRank Calculation in Action**

Let’s assume that we have a PR5 website that has 49 links on it, and we are considering receiving a link from this website. We want to figure out using the formula above how a single link would benefit our website and the overall pagerank we may achieve from it.

32768 * 085 / 50(links 49 + 1 our new one) = 557 PR pts

We compare this to the table expressed above and 557 is closes to the 512 PR points for PR3. Therefore a single link form a PR 5 website with 50 outgoing links will most likely result in a PR3 page if no other links are involved to your site.

This information is crucial, even though it is a rough estimate and not exact it still is close enough to need to use it. This will allow you to analyze if a link exchange program is beneficial for your website, especially if you already have a high PR page. Understanding the algorithm is crucial to SERP success! Roughly 85% of the PR of a web page is transferred to the web pages it links to, shared equally among the links. Do you understand the significance of that statement? Most people don’t understand the whole linking process and algorithm. Understand it and use it! Links are the backbone of your website and the websites PR. It isn’t all about the PR of a website if that website is throwing away 200 links on that page! So do the math and figure out where/what the best websites are to link with.

[tags]pagerank analyzed, pagerank algorithm, pagerank calculations, pagerank math, pagerank help[/tags]

Nice test, I was recently thinking about writing an automated unit test suite in Django to run a whole bunch of tests against Google ranking and indexing patterns.