MPageRank: The Stability of Web Graph

Received November 04, 2008Abstract. Problems which have a huge database always issue challenges to scientists.Evaluating importance of Webs is an interesting example. This problem should be verydifficult about not only computation, but also storage since the Web environment con-tains around 10 billions Web pages. Basing on the “random surfer” idea of PageRankalgorithm, MPageRank greatly improves results of Web search by applying a proba-bilistic model on the link structure of Webs to evaluate “authority” of Webs. UnlikePageRank, in MPageRank, a Web now has different ranking scores which depend onthe given multi topics. By assigning a value characterizing a relationship between con-tent of pages and a popular topic, we would like to introduce some new notions suchas the influence of page and the stability of rank score vector to evaluate the stabilityof Web environment. However, the main idea of establishing the MPageRank modelis to partition our Web graph into smaller-size Web subgraphs. As a consequence ofevaluation and rejection about pages influence weakly to other pages, the rank scoreof pages of the original Web graph can be approximated from the rank score of pagesin the new partition Web graph.2000 Mathematics Subject Classification: ————————–.Key words: —————————————-.