Page Rank Implementation in Search Engine

Abstract

A user does not have the ability or patience to scan through all pages that contain the given query words. One expects the relevant pages to be displayed within the top 20-30 pages returned by the search engine and hence some page rank algorithm is required. Modern search engines employ methods of ranking the results to provide the "best" results first that are more elaborate than just plaintext ranking. One of the most known and influential algorithms for computing the relevance of web pages is the Page Rank algorithm used by the Google search engine. It was invented by Larry Page and Sergey Brin while they were graduate students at Stanford, and it became a Google trademark in 1998. The idea that Page Rank brought up was that, the importance of any web page can be judged by looking at the pages that link to it. If we create a web page i and include a hyperlink to the web page j, this means that we consider “j” important and relevant for our topic. If there are a lot of pages that link to j, this means that the common belief is that page j is important. The web is very heterogeneous by its nature, and certainly huge, so we do not expect its graph to be connected. Likewise, there will be pages that are plain descriptive and contain no outgoing links. So, the solution was given by Page and Brin. We see that PageRank does not rank web sites as a whole, but is determined for each page individually. Further, the PageRank of page A is recursively defined by the PageRanks of those pages which link to page A.The PageRank of pages Ti which link to page A does not influence the PageRank of page A uniformly. Within the PageRank algorithm, the PageRank of a page T is always weighted by the number of outbound links C(T) on page T. This means that the more outbound links a page T has, the less will page A benefit from a link to it on page T. The weighted PageRank of pages Ti is then added up. The outcome of this is that an additional inbound link for page A will always increase page A's PageRank. Finally, the sum of the weighted PageRanks of all pages Ti is multiplied with a damping factor d which can be set between 0 and 1. Thereby, the extend of PageRank benefit for a page by another page linking to it is reduced.