

Google Page Rank Explained
Page Rank (PR) is an algorithm used by Google to compute the relative importance of a particular webpage on the internet and assign it a numeric value from 0 (least important) to 10 (most important). This value is calculated through an iterative analysis of the backlinks to the webpage. If webpage A links to webpage B then webpage B would receive 1 "vote" towards their page rank.
Fact: Page Rank is calculated on a webpage by webpage basis not on a website by website basis
The importance of the webpage casting a vote and the total number of outgoing links on the webpage casting a vote are the primary factors which determine how much "voting share " this webpage will transfer to each of the outgoing links on them. Google calculates a webpage's page rank by adding up all of the "voting shares " for that webpage through an iterative calculation.
Page Rank is one of the factors Google utilizes to help determine their Search Engine Ranking Positions (SERP's). It should be noted that this algorithm is only one part of their overall ranking scheme and not necessarily the most important one as many website's would have you believe. The general internet user has no idea about the concept of page rank and are unable to tell what a particular page's PR is unless they have the Google Toolbar installed (or use an online page rank checker). Since page rank is part of Google's search ranking algorithm an understanding of the concept is still important for any webmaster concerned with getting traffic to their site.
Fact: Not all links pointing to a webpage are counted as votes for that webpage
As soon as Google introduced the concept of page rank unsavory webmasters developed ways to manipulate the rankings. These webmasters began creating web pages with the sole purpose of increasing the amount of incoming links pointing to their website.
Common Black Hat SEO Techniques:
 Link Farms  pages containing long lists of unrelated links set up for the sole purpose of manipulating search engine rankings and page rank
 Doorway Pages  orphaned webpages either on the same website or distributed throughout the internet stuffed with keywords containing links to the offender's site. Used to artificially inflate the back link count for a website.
 Free For All Links Pages  a type of link farm where, as the name implies, anyone is free to post their link. Once a valuable way to spread the word about your website, abuse through auto submissions has rendered these sites worthless and are now viewed as search engine SPAM.
 Automated or Hosted Link Exchanges  sites that offer to provide "hundreds" of back links to your site instantly. Generally you will have to install some html code on your website to display their directory and in return anyone else who has this code installed on their website will be displaying your link. This is a case where "if it sounds too good to be true it is". The search engine's are wise to this technique and watch for unnatural "spikes" in the number of backlinks pointing to a website. In actuality it is possible to inflate your page rank with this technique but if the search engine's wise up to your practices (and they always do eventually) you risk being dropped from their index or black holed in their rankings.
How is Page Rank Calculated?
When Google introduced the concept of page rank they published the algorithm they were going to use to calculate it. The formula in it's current form is known only to the engineers at Google but it is fair to say it closely resembles the following formula.
PR(A) = (1d) + d(PR(t1)/C(t1) + ... + PR(tn)/C(tn))
While at first glance this equation can seem daunting, in actuality the concept is not that hard to understand. Let's take a minute to break down the formula and see what conclusions can be drawn.
PR(t1)...PR(tn)  the page rank (PR) of each page from page t1 to tn. (each value of t represents 1 link to webpage A)
C(t1)...C(tn)  the number of outgoing links (C) on each page from page t1 to tn
d  damping factor
Quoting from the original Google Page Rank white paper:
The parameter d is a damping factor which can be set between 0 and 1. We usually set d to 0.85.
Knowing what these parameters mean and knowing the value of the damping factor we can simplify the formula from above:
PR(A) = 0.15 + 0.85*(A "share" of the PR of every webpage linking to page A)
The "share" each webpage passes to webpage A can be computed by dividing the Page Rank of the webpage linking to page A by the number of outgoing links on that page. Each outgoing link on that page would receive an equal voting share from the total available page rank of the page containing the outgoing link. The total available page rank each webpage has available to transfer to outgoing links is a little less than the total page rank of that page (PR of page * 0.85) which can be easily derived when the damping factor is known.
Implications
Having a basic understanding of the algorithm we can now draw a few conclusions about page rank and it's implications to your website. For instance, it is very possible to have a link on web page X that has a high page rank transferring less page rank voting shares to your website than a link on web page Y with a lower page rank.
How is this possible? Let's analyze an example:
Page X  page rank 4, outgoing links 10
Page Y  page rank 8, outgoing links 100
Page X would transfer 0.85(4/10) = 0.34 page rank voting shares to each outgoing link
Page Y would transfer 0.85(8/100) = 0.068 page rank voting shares to each outgoing link
Even though Page X has a much lower page rank value, due to the fact that the number of outgoing links on Page X is so much smaller than on Page Y it actually transfers more page rank voting shares to each outgoing link than Page Y .
Pages with no links back to them would still have a modest page rank value of 0.15 derived from the (1d) portion of the equation. It is important to note that while this value holds true according to the equation, only Google engineers are privy to the knowledge of whether actual page rank voting share is transferred in this scenario. Google could easily say that pages with no incoming links transfer a page rank voting share of 0 with a click of a mouse and no one would know for sure except them.
Fact: The Google Toolbar displays Page Rank as a base 10 log scale that is not the "actual" result of the Page Rank calculation
The average page rank of all pages in the index is 1. It is possible to have an "actual" page rank value in the millions or much smaller than 1 using the page rank formula but the Google toolbar only displays integers from 0  10 on it's pr meter. Only Google knows how the scale is split up and where the basepoints for each level are. For example, it may take an actual page rank of 10,000 using the formula above to achieve a page rank of 4/10 on the toolbar scale.
Page Rank in Complex Networks
The example above does not actually duplicate a real world example since it is only computing the page rank "voting share" of the ffa page in an idealized situation where the page rank of the page is already known. In complex networks with links in and links out of webpages the actual page rank for a webpage cannot be known due to the interdependencies each web page has on one another to calculate their page rank.
Think of it as a "chicken and the egg" situation. The problem can be solved by taking a best initial guess for the page rank value of each webpage in the network and plugging it into the page rank formula. The results of these calculations are then used to calculate the next incremental page rank values for the webpages in the network. This calculation is repeated over and over again until the page rank value approaches a limit. This limit is then the actual page rank for that page. In a complex network like the internet finding the page rank for all webpages can take millions of iterations.
Click here for more detailed examples and an online page rank calculator
It is also worth noting that when a webpage transfers page rank voting shares to another webpage the page rank of the contributing page is not reduced in any way. There is no actual page rank transfer, only a weighted "vote" is passed to the outgoing links.
Links on webpages with a high page rank and little or no other outgoing links on them but yours will provide the best opportunities to improve your page rank (if that is your goal and it shouldn't be, link for traffic not pr). Make sure to work on your site content and design before approaching other webmasters for links. The bottom line is you need to have a site worth linking to in order to get people to link to it.
Resources
Google Page Rank Whitepaper
Complex Page Rank Examples including Calculations








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