### Citations

4668 | The anatomy of a large-scale hypertextual Web search engine
- Brin, Page
- 1998
(Show Context)
Citation Context ...onstruct a matrix capturing thesWeb hyperlink structure and compute a measures of pages popularity (ranks) usingslinear algebra methods.s75s2. The PageRank algorithmsIn well-known study Brin and Page =-=[3]-=- have proposed an algorithm for determining the ranking of Web pages called PageRank , which uses the term "weightsofspage". According to this proposal the weight of page depends on the number ofsothe... |

3629 | Authoritative sources in a hyperlinked environment
- Kleinberg
- 1999
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Citation Context ... Web pages based onstheir text content or on the hyperlink structure of the Web. This paper describes algorithms that use the hyperlink structure, called link-based algorithms: PageRanks[12] and HITS =-=[8]-=-. The basic notion for these algorithms is the Web graph, whichsis a digraph with a node for each Web page and an arc between pages i and j ifsthere is a hyperlink from page i to page j. Given a colle... |

3266 | The pagerank citation ranking: Bringing order to the web
- Page, Brin, et al.
- 1998
(Show Context)
Citation Context ...rithms to sort Web pages based onstheir text content or on the hyperlink structure of the Web. This paper describes algorithms that use the hyperlink structure, called link-based algorithms: PageRanks=-=[12]-=- and HITS [8]. The basic notion for these algorithms is the Web graph, whichsis a digraph with a node for each Web page and an arc between pages i and j ifsthere is a hyperlink from page i to page j. ... |

758 |
Matrix Analysis and Applied Linear Algebra
- Meyer
- 2000
(Show Context)
Citation Context ...)swhere 0<α<1, /n1)(1=E T ⋅sand T1 , 1 are, respectively, the column and rowsvectors of all 1’s.sBecause G is stochastic (i.e., the entries in each column sum to 1), the dominant eigenvalue of G is 1 =-=[11]-=-. Notice, also, that matrix G is completely positive,si.e. all elements of G are positive, although the probability of transitioning may besvery small in some cases, it is always nonzero. The irreduci... |

243 |
Accessibility of information on the web
- Lawrence, Giles
- 1999
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Citation Context ...tes size ofsthe Internet can be estimated at tens of terabytes. The Internet is characterized by asvery high dynamics of change in its size and structure. The research conducted bysLawrence and Giles =-=[10]-=- shows that the size of the Web has doubled in the last twosyears. Large is the dynamics of Internet content . In addition to the newly createdspages, existing pages are constantly updated. Research c... |

162 | Searching the web.
- Arasu, Cho, et al.
- 2001
(Show Context)
Citation Context ...o rank thesresults of the query. This page rank, however, would be little resistance to a phenomenon known as spam, because it is quite easy to artificially create multiplespages pointing to the page =-=[1]-=-. To counteract such practices PageRank algorithmsextends the basic idea of citations, taking into account the importance of each pagesthat point to thesanalyzed page. This means that the definition o... |

149 | H.: Estimating frequency of change
- Cho, Garcia-Molina
- 2003
(Show Context)
Citation Context ...% of all the pages available on the Web is updated daily. Knowledge of the structure and size of the Internet and development ofsmethods for Internet structure modeling is a number of ongoing studies =-=[4]-=-.sThere are two main reasons why the traditional information retrieval techniques may not be sufficiently effective in the exploration of the modern Internet.sThe first reason stems from the mentioned... |

36 |
Loan,Matrix computations, 2nd ed.
- Golub, V
- 1989
(Show Context)
Citation Context ...sing A alone might not converge properly. It can cycle or theslimit may be dependent on the starting vector. Part of the explanation for this is thats77sthe matrix A is not yet necessarily stochastic =-=[6]-=-. For example, if some page is asleak node than corresponding row of the matrix A contains all zeros (0).sThus, to ensure that matrix A is stochastic, we must ensure that every rowssums to 1. It can b... |

5 |
How to Do Everything with Google.
- Blachman, Fredricksen, et al.
- 2003
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Citation Context ...perlinking structure. Thus, link analysis has become the means to ranking. One successful and well-publicized linkbased ranking system is PageRank, the ranking system used by the Google searchsengine =-=[2]-=-.sFrom the foregoing considerations, it follows that there is possibility ofspractical achieve time savings associated with the ranking Web pages, byssubstituting the result (page ranking), obtained t... |

2 |
Google’s index nearly doubles
- Coughran
- 2005
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Citation Context ...periments [7] indicate that the ordering induced by the PageRank converges much faster than the actual PageRank.sWhen dealing with data sets as large as Google uses (more than eight billionsweb pages =-=[5]-=-), it is unrealistic to form a matrix G and find its dominant eigenvector. It is more efficient to compute the PageRank vector using the power methodsvariant, where we can compute the PageRank vector ... |

1 |
Efficient computation of PageRank
- Havelivala
- 1999
(Show Context)
Citation Context ...(since this is used to rank thespages) than the actual PageRank values themselves [1]. Thus, we can terminate thespower iteration once the ordering of the pages becomes reasonably stable. Experiments =-=[7]-=- indicate that the ordering induced by the PageRank converges much faster than the actual PageRank.sWhen dealing with data sets as large as Google uses (more than eight billionsweb pages [5]), it is u... |

1 |
The Use of the Linear Algebra by Web Search Engines, http://meyer.math.ncsu.edu/Meyer/PS_Files/IMAGE.pdf
- Langville, Meyer
- 2004
(Show Context)
Citation Context ...ity to estimate the number of iterations required to reach a tolerance levelsmeasured by 1)(k(k) rr −− . The number of needed iterations k is approximatelyslog ε / log α , where εsthe tolerance level =-=[9]-=-.sIt is worth noting that the founders of Google, Lawrence Page and SergeysBrin, use α = 0.85 and find success with only 50 to 100 power iterations [9].s79s3. Test the effectiveness of the PageRank al... |