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PageRank is a numeric value between 1-10 describing the "importance" of a URL (web page), and is determined by Google. It is noteworthy, that pages, that have a high PageRank number are more likely to appear at the top of the search results.
Some very basic, yet important aspects, that Google uses in determining PageRank is the uniqueness and authority of a site's content. Sites that demonstrate these qualities will also often have a number of other websites, who share the same interest, link to them. These links are important as each one of these links act as a "vote, for a site's content. The quality of these votes are in turn determined by the PageRank of those particular pages voting, (linking).
Therefore, if votes, (links), come from other pages that have high PageRanks, they are considered to have greater value and will in return, actually give the linked page greater value as well and contribute to increasing that URL's PageRank. This is where it is very helpful to use PageRank Checker to potentially find quality sites.
To sum it up in simple terms, high ranking URL's are ones that demonstrate a high degree of authority on subject matter. They are defined as popular, characterized by having many one way links coming from other high ranking URL's. High ranking URL's primarily link to other High ranking URL's that offer very relevant information, unique points of view or contributions, and provide the user with a speed optimized experience in order to maintain their own good standing.
Google's algorithm, using PageRanks (out of 100) for a simple network:
Using the circles, labeled A through F in the diagram below to represent web pages, we can see how a URL's PageRank is calculated*.
In this instance, Page C has a higher PageRank than Page E, even though it has the fewest links to it. The algorithm has determined in this case that the link it has is of a much higher value, and we'll explain why;
The algorithm tells us that a web surfer that chooses a random link on every page, and does so, but with a 15% likelihood of jumping to a random page on the whole web, but will actually end up staying on Page E for 8.1% of the time due to the directional linking relationships.
The 15% likelihood of jumping to an arbitrary page, according to the algorithm, corresponds to a damping factor of 85%. It is determined that without this damping factor, all web surfers would eventually end up mostly visiting Pages A, B, or C, leaving all other pages with a PageRank of zero.
It is interesting to note that even though Page A has no outgoing links, it is logical to assume, that A is still invariably linked to all pages in the web simply by this one inbound link.
* PageRanks reported by Google are rescaled logarithmically