By Abraham D. Flaxman, Juan Vera (auth.), Anthony Bonato, Fan R. K. Chung (eds.)

This e-book constitutes the refereed lawsuits of the fifth foreign Workshop on Algorithms and versions for the Web-Graph, WAW 2007, held in San Diego, CA, united states, in December 2007 - colocated with WINE 2007, the 3rd overseas Workshop on web and community Economics.

The thirteen revised complete papers and 5 revised brief papers offered have been rigorously reviewed and chosen from a wide pool of submissions for inclusion within the ebook. The papers tackle a wide selection of subject matters relating to the research of the Web-graph corresponding to random graph types for the Web-graph, PageRank research and computation, decentralized seek, neighborhood partitioning algorithms, and traceroute sampling.

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Extra resources for Algorithms and Models for the Web-Graph: 5th International Workshop, WAW 2007, San Diego, CA, USA, December 11-12, 2007. Proceedings

Example text

F = F1 , β = 2: η = lnlnlnnn , ϕ = O(η). We now consider the connectivity and diameter of Gn . For this we will place some more restrictions on F . Define the parameter ρ(μ) by Iρ = μI. We will say that F is smooth (for some value of μ) if (S1) F is monotone non-increasing. (S2) ρ2 n ≥ L ln n for some sufficiently large constant L. (S3) ρ2 F (2ρ) ≥ c3 I for some c3 which is bounded away from zero. (4) A Geometric Preferential Attachment Model of Networks II 45 Theorem 2. Suppose that α > 2 and F is smooth for some constant μ > 0 and m ≥ K ln n for K sufficiently large.

Pham 1−c T 1 [I − cW ]−1 n as a system of three linear equations: π= (5) c 1−c T πDN 11T = 1 , n n c 1−c T 1 , πIN+SCC [I − cP ] − πDN 11T = n n c 1−c T 1 . − πIN+SCC cS + πDN − πDN 11T = n n πOUT [I − cQ] − πIN+SCC cR − (6) (7) (8) Solving (6–8) for πIN+SCC we obtain πIN+SCC (c) = (1 − c)α c2 α uIN+SCC I − cP − S1uIN+SCC 1 − cβ 1 − cβ −1 , (9) where α = |IN + SCC|/n and β = |DN|/n are the fractions of nodes in IN+SCC and DN, respectively, and uIN+SCC = |IN + SCC|−1 1T is a uniform probability row-vector of dimension |IN + SCC|.

Finally, we draw the attention of the reader to the fact that choosing c = 1/2 also significantly reduces the gap between the ranking by PageRank and the ranking by the number of clicks. Table 2. Comparison between PR and click based rankings c PR rank w/o link PR rank with link rank by no. 85, the Pure OUT component receives an unfairly large share of the PageRank mass. Remarkably, in order to satisfy any of the three intuitive criteria of fairness presented above, the value of c should be drastically reduced.

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