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Vietnam
Journal of Mathematics 37:4 (2009) 475-489
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MPageRank: The Stability of Web Graph
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Le Trung Kien, Le
Trung Hieu, Tran Loc Hung, and Le Anh Vu
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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.
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2000 Mathematics Subject Classification: 68W40, 05C75.
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Keywords: MPageRank algorithm, web graph, ranking
web, probabilistic model.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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