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Google PageRank Formula |
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Google pagerank formula. This formula is used by Google to rank websites. If you understands this formula , it means you can easily rank your site in Google good ranking. |
Simplified
Suppose a small universe of four web pages: A, B, C and D. If all those pages link to A, then the PR (PageRank) of page A would be the sum of the PR of pages B, C and D.
PR(A) = PR(B) + PR(C) + PR(D)
But then suppose page B also has a link to page C, and page D has links to all three pages. One cannot vote twice, and for that reason it is considered that page B has given half a vote to each. In the same logic, only one third of D's vote is counted for A's PageRank.
In other words, divide the PR by the total number of links that come from the page.
Finally, all of this is reduced by a certain percentage by multiplying it by a factor q. For reasons explained below, no page can have a PageRank of 0. As such, Google performs a mathematical operation and gives everyone a minimum of 1 - q. It means that if you reduced 15% everyone you give them back 0.15.
So one page's PageRank is calculated by the PageRank of other pages. Google is always recalculating the PageRanks. If you give all pages a PageRank of any number (except 0) and constantly recalculate everything, all PageRanks will change and tend to stabilize at some point. It is at this point where the PageRank is used by the search engine
Complex formula
The formula uses a model of a random surfer who gets bored after several clicks and switches to a random page. The PageRank value of a page reflects the frequency of hits on that page by the random surfer. It can be understood as a Markov process in which the states are pages, and the transitions are all equally probable and are the links between pages. If a page has no links to another pages, it becomes a sink and therefore makes this whole thing unusable, because the sink pages will trap the random visitors forever. However, the solution is quite simple. If the random surfer arrives to a sink page, it picks another URL at random and continues surfing again.
To be fair with pages that are not sinks, these random transitions are added to all nodes in the Web, with a residual probability of usually q=0.15, estimated from the frequency that an average surfer uses his or her browser's bookmark feature.
So, the equation is as follows:
where p1,p2,...,pN are the pages under consideration, L(pi) is the set of pages that link to pi, and N is the total number of pages.
The PageRank values are the entries of the dominant eigenvector of the modified adjacency matrix. This makes PageRank a particularly elegant metric: the eigenvector is
where R is the solution of the equation
 where the adjacency function is 0 if page pi does not link to pj, and normalised such that, for each i
The values of the PageRank eigenvector are fast to approximate (only a few iterations are needed) and in practice it gives good results.
As a result of Markov theory, it can be shown that the PageRank of a page is the probability of being at that page after lots of clicks. This happens to equal t - 1 where t is the expectation of the number of clicks (or random jumps) required to get from the page back to itself.
The main disadvantage is that it favors older pages, because a new page, even a very good one, will not have many links unless it is part of an existing site (a site being a densely connected set of pages).
That's why PageRank should be combined with textual analysis or other ranking methods. PageRank seems to favor Wikipedia pages, often putting them high or at the top of searches for several encyclopedic topics. A common theory is that this is because Wikipedia is very interconnected, with each article having many internal links from other articles, which in turn have links from many other sites on the Web pointing to them. Compared to Wikipedia, and similar high quality content-rich sites, the rest of the World Wide Web is relatively loosely connected
The Implementation of PageRank in the Google Search Engine
Regarding the implementation of PageRank, first of all, it is important how PageRank is integrated into the general ranking of web pages by the Google search engine. The proceedings have been described by Lawrencec Page and Sergey Brin in several publications. Initially, the ranking of web pages by the Google search engine was determined by three factors:
- Page specific factors
- Anchor text of inbound links
- PageRank
Page specific factors are, besides the body text, for instance the content of the title tag or the URL of the document. It is more than likely that since the publications of Page and Brin more factors have joined the ranking methods of the Google search engine. But this shall not be of interest here.
In order to provide search results, Google computes an IR score out of page specific factors and the anchor text of inbound links of a page, which is weighted by position and accentuation of the search term within the document. This way the relevance of a document for a query is determined. The IR-score is then combined with PageRank as an indicator for the general importance of the page. To combine the IR score with PageRank the two values are multiplicated. It is obvious that they cannot be added, since otherwise pages with a very high PageRank would rank high in search results even if the page is not related to the search query.
Especially for queries consisting of two or more search terms, there is a far bigger influence of the content related ranking criteria, whereas the impact of PageRank is mainly visible for unspecific single word queries. If webmasters target search phrases of two or more words it is possible for them to achieve better rankings than pages with high PageRank by means of classical search engine optimisation.
If pages are optimised for highly competitive search terms, it is essential for good rankings to have a high PageRank, even if a page is well optimised in terms of classical search engine optimisation. The reason therefore is that the increase of IR score deminishes the more often the keyword occurs within the document or the anchor texts of inbound links to avoid spam by extensive keyword repetition. Thereby, the potentialities of classical search engine optimisation are limited and PageRank becomes the decisive factor in highly competitive areas.
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