Web. Web p OutDegree(p) log 7 1/OutDegree(p) A New Difinition of Subjective Distance between Web Pages

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1 Vol. 44 No. 1 Jan Web 1 2, 3 4 Web p OutDegree(p) log 7 1/OutDegree(p) A New Difinition of Subjective Distance between Web Pages Yutaka Matsuo, 1 Yukio Ohsawa 2, 3 and Mitsuru Ishizuka 4 The pages and hyperlinks of the World Wide Web may be viewed as nodes and edges in a directed graph. In this paper, we propose a new definition of the distance between two pages, called average-clicks. It is based on the probability to click a link through random surfing. We compare the average-clicks measure to the classical measure of clicks between two pages, and show the average-clicks fits better to the users intuitions of distance. 1. World Wide Web Web 2) Web Google PageRank 5) hub authority Kleinberg 10) Web 12) 2 1 National Institute of Advanced Industrial Science and Technology 2 Japan Science and Technology Corporation 3 The University of Tsukuba 4 The University of Tokyo 14) 8) 1 7) 1) Web 19 outlink outlink 11) outlink 1

2 2 Jan (clicks) (average-clicks) Web p OutDegree(p) URL OutDegree(p) log(outdegree(p)) (1) 1 1 a 1 2 a log a =loga 2 18) (1) 2.1 () p log n (OutDegree(p)) (2) OutDegree(p) html 7 3) log n () n =7 (2) p q 2.3 () p q p q p q 1 A 3 log 7 (1/3) 0.56 B 7 1 A C 1.56 A D 2 F 1 0 Yahoo! ) 7 e

3 Vol. 44 No. 1 Web 3 1 -log7 -= A B 1 -log7 -= C From A to C, 1.56 average-click, 2 clicks. b c a e a b c e 0.56 E 0.36 F 0 D From A to D, 0.92 average-click, 2 clicks. d d Yahoo! Yahoo! ( r ) a r (2 7 r 1) p a r a a ( 2) r a 1/7 r 7 r r function Search Shortest Path (s, t, d thre ) α 1.0, n 7. list Add List(s, empty), d(s) 0. p s while p t Fetch page p and extract links which points to page p k (k =1,...,n p) for k 1 to n p d(p k ) d(p) log n(α/n p) if d(p k ) >d thre then next list Add List(p k,list) end if list is empty return failure p Choose Minimal(list, d) end return d(t) Add List(a, list) list a. Choose Minimal(list, d) d(a) a list. d thre query focused crawling 7) 3. Web

4 4 Jan To URL / 1.62 / 2 matumura/ Yahoo! 3.02 / matsuo / matsuo/ 0.0 IJCAI 5.39 / J 4.03 / / s t ) 2 matsuo/ Yahoo! IJCAI J URL URL URL 1 4, ) ) 1 4

5 Vol. 44 No. 1 Web ??? ) p OutDegree(p) α/outdegree(p) 1 α ( URL Web α 0 1 Google PageRank Web 17)

6 6 Jan log n (α/outdegree(p)) α Web PageRank α =0.85 α =1 α <1 1 0 α<1 9) 4) 19) 6) href 1 Web 3) Web Web 5. 13) 1) Adamic, L. A.: The Small World Web, Proc. ECDL 99, pp (1999). 2) Adamic, L. A. and Adar, E.: Friends and Neighbors on the Web (to appear). URL:// shl/papers/web10/fnn.pdf. 3) Bharat, K. and Broder, A.: A technique for measuring the relative size and overlap of public Web search engines, Proc. 7th WWW Conf. (1998). 4) Botafogo, R. A., Rivlin, E. and Schneiderman, B.: Structural Analysis of Hypertexts: Identifying Hierarchies and Usefule Metrics, ACM Transaction on Information Systems, Vol. 10, No. 2 (1992). 5) Brin, S. and Page, L.: The Anatomy of a Large-Scale Hypertextual Web Search Engine, Proc. 7th WWW Conf. (1998).

7 Vol. 44 No. 1 Web 7 6) Chakrabarti, S., Dom, B., Raghavan, P., Rajagopalan, S., Gibson, D. and Kleinberg, J.: Automatic resource compilation by analyzing hyperlink structure and associated text, Proc. 7th WWW Conf. (1998). 7) Chakrabarti, S., van den Berg, M. and Dom, B.: Focused crawling: a new approach to topic-specific Web resource discovery, Proc. 8th WWW Conf. (1999). 8) Flake, G. W., Lawrence, S. and Giles, C. L.: Efficient Identification of Web Communities, Proc. ACM SIGKDD-2000, pp (2000). 9) :,, chapter 6 (1996). 10) Kleinberg, J.: The Small-World Phenomenon: An Algorithmic Perspective, Technical Report TR , Cornell University (1999). 11) Kleinberg, J. M., Kumar, R., Raghavan, P., Rajagopalan, S. and Tomkins, A. S.: The Web as a graph: measurements, models, and methods, Proc. International Conf. on Combinatorics and Computing (1999). 12) Kumar, S. R., Raghavan, P., Rajagopalan, S. and Tokins, A.: Trawling the web for emerging cyber communities, Proc. 8th WWW Conf. (1999). 13) Lawrence, S.: Context in Web Search, IEEE Data Engineering Bulletin, Vol. 23, No. 3, pp (2000). 14) : Web,, Vol. 16, No. 3, pp (2001). 15) Murray, B. and Moore, A.: Sizing the Internet, White paper, Cyveillance, Inc. (2000). ( 16)Najork,M.andWiener,J.L.:Breadth-first search crawling yields high-quality pages, Proc. 10th WWW Conf. (2001). 17) Page, L., Brin, S., Motwani, R. and Winograd, T.: The PageRank Citation Ranking: Bringing order to the Web, Technical report, Stanford University (1998). 18) Shannon, C. E.: A mathematical theory of communication, Bell System Technical Journal, Vol. 27, pp and (1948). 19) Spertus, E.: ParaSite: Mining Structural Information on the Web, Proc. 6th WWW Conf. (1997). ( ) ( ) AAAI AAAI IEEE NTT IEEE AAAI

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