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The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element E is also called the PageRank of E and denoted by PR(E).
PageRank was developed at Stanford University by Larry Page (hence the name Page-Rank) and Sergey Brin as part of a research project about a new kind of search engine.
The project started in 1995 and led to a functional prototype, named Google, in 1998. Shortly after, Page and Brin founded Google Inc., the company behind the Google search engine. While just one of many factors which determine the ranking of Google search results, PageRank continues to provide the basis for all of Google's web search tools.
The name PageRank is a trademark of Google. The PageRank process has been patented (U.S. Patent 6,285,999 ). The patent is not assigned to Google but to Stanford University.
PageRank is a probability distribution used to represent the likelihood that a person randomly clicking on links will arrive at any particular page. PageRank can be calculated for any-size collection of documents. It is assumed in several research papers that the distribution is evenly divided between all documents in the collection at the beginning of the computational process. The PageRank computations require several passes, called "iterations", through the collection to adjust approximate PageRank values to more closely reflect the theoretical true value.
A probability is expressed as a numeric value between 0 and 1. A 0.5 probability is commonly expressed as a "50% chance" of something happening. Hence, a PageRank of 0.5 means there is a 50% chance that a person clicking on a random link will be directed to the document with the 0.5 PageRank.Source: Wikipedia