Algorithms and Models for the Web Graph: 9th International by Fan Chung, Alexander Tsiatas (auth.), Anthony Bonato,

By Fan Chung, Alexander Tsiatas (auth.), Anthony Bonato, Jeannette Janssen (eds.)

This ebook constitutes the refereed complaints of the ninth foreign Workshop on Algorithms and versions for the Web-Graph, WAW 2012, held in Halifax, Nova Scotia, Canada, in June 2012. The thirteen papers provided have been conscientiously reviewed and chosen for inclusion during this quantity. They deal with a couple of issues with regards to the complicated networks such hypergraph coloring video games and voter versions; algorithms for detecting nodes with huge levels; random Appolonian networks; and a sublinear set of rules for Pagerank computations.

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Extra info for Algorithms and Models for the Web Graph: 9th International Workshop, WAW 2012, Halifax, NS, Canada, June 22-23, 2012. Proceedings

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Cooper, A. Frieze, and P. Pralat Proof. For a contradiction suppose that k = deg− (vi , s) ≥ (2ω log t)(s/i)pA1 for some value of s (i ≤ s ≤ t). Since k ≥ ω log t, Theorem 2 can be applied to get that deg− (vi , i) = (1 + o(1)) = (1 + o(1))k pA1 i A2 A1 = (1+ o(1)) f −1 (k) s i −pA1 A2 A1 s −1 f (k) pA1 s i −pA1 ≥ (2 + o(1))ω log t, which is clearly a contradiction (in fact, deg− (vi , i) = 0). 3 Directed Diameter The small world property, introduced by Watts and Strogatz [29], is a central notion in the study of complex networks (see also [22]).

In the latter case, u links to v with probability p. The SPA model incorporates the principle of preferential attachment, since vertices with a higher in-degree will have a larger sphere of influence. We investigate the (directed) diameter, small separators, and the (weak) giant component of the model. 2 The SPA Model We start by giving a precise description of the SPA model, presenting some known properties, and deriving some facts about the model, which we will need to prove our results. In [3] (see also [4] for a proceeding version of this paper), the model is defined for a variety of metric spaces S.

In: Proceedings of the 16th International Conference on World Wide Web (2007) 3. : A spatial web graph model with local influence regions. Internet Mathematics 5, 175–196 (2009) 4. : A Spatial Web Graph Model with Local Influence Regions. K. ) WAW 2007. LNCS, vol. 4863, pp. 96–107. Springer, Heidelberg (2007) 5. : Emergence of scaling in random networks. Science 286, 509–512 (1999) 6. : Compact Representations of Separable Graphs. In: Proc. of ACM/SIAM Symposium on Discrete Algorithms, pp. 679–688 (2003) 7.

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