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Vietnam Journal of Mathematics 37:4 (2009) 475-489  

MPageRank: The Stability of Web Graph

Le Trung Kien, Le Trung Hieu, Tran Loc Hung, and Le Anh Vu

Abstract.  Problems which have a huge database always issue challenges to scientists. Evaluating importance of Webs is an interesting example. This problem should be very difficult about not only computation, but also storage since the Web environment contains around 10 billions Web pages. Basing on the ``random surfer" idea of PageRank algorithm, MPageRank greatly improves results of Web search by applying a probabilistic model on the link structure of Webs to evaluate ``authority" of Webs. Unlike PageRank, in MPageRank, a Web now has different ranking scores which depend on the given multi topics. By assigning a value characterizing a relationship between content of pages and a popular topic, we would like to introduce some new notions such as the influence of page and the stability of rank score vector to evaluate the stability of Web environment. However, the main idea of establishing the MPageRank model is to partition our Web graph into smaller-size Web subgraphs. As a consequence of evaluation and rejection about pages influence weakly to other pages, the rank score of pages of the original Web graph can be approximated from the rank score of pages in the new partition Web graph.

2000 Mathematics Subject Classification: 68W40, 05C75.

Keywords: MPageRank algorithm, web graph, ranking web, probabilistic model.

 

 

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