Abstract
In this paper we discuss three important kinds of Markov chains used in Web search algorithms-the maximal irreducible Markov chain, the minimal irreducible Markov chain and the middle irreducible Markov chain. We discuss the stationary distributions, the convergence rates and the Maclaurin series of the stationary distributions of the three kinds of Markov chains. Among other things, our results show that the maximal and minimal Markov chains have the same stationary distribution and that the stationary distribution of the middle Markov chain reflects the real Web structure more objectively. Our results also prove that the maximal and middle Markov chains have the same convergence rate and that the maximal Markov chain converges faster than the minimal Markov chain when the damping factor \( \alpha > \frac{1} {{{\sqrt 2 }}} \).
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Bianchini, M., Gori, M., Scarselli, F. Inside pagerank. ACM Transactions on Internet Technology, 2(5): 92–128 (2005)
Boldi, P., Santini, M., Vigna, S. PageRank as a function of the damping factor. In the 14th International World Wide Web Conference 2005, http://www2005.org/cdrom/docs/p557.pdf.
Border, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S.,Stata, R.,Tomkins, A.,Wiener, J. Graph structure in the Web. In the 9th International World Wide Web Conference, May, 2000
Brin, S., Page, L., Motwami, R., Winograd, T. The pagerank citation ranking: bringing order to the web. Technical report, Standford digital library technologies project, Stanford University, Stanford, CA, USA, 1998
Golub, G.H., Van Loan, C.F. Matrix computions. Johns Hopkins University Press, Baltimore MD, 1984
Langville, A.N., Meyer, C.D. Deeper inside pagerank. Internet Mathematics, 1(3): 355–400 (2004)
Qian, M.,Gong, G. The theory of stochastic process (the second edition). Peking University Press, Beijing, 1997
Zhu, Z.H., Bao, Y. Comparison of two web search algorithms. Acta Mathematicae Applicatae Sinica, 28(4): 577–586 (2005) (in Chinese)
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Supported by the National Natural Science Foundation of China (No.10371034).
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Bao, Y., Zhu, Zh. Comparison of Three Web Search Algorithms. Acta Math. Appl. Sin, Engl. Ser. 22, 517–528 (2006). https://doi.org/10.1007/s10255-006-0327-2
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DOI: https://doi.org/10.1007/s10255-006-0327-2