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.
Read or Download Algorithms and Models for the Web Graph: 9th International Workshop, WAW 2012, Halifax, NS, Canada, June 22-23, 2012. Proceedings PDF
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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
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 , is a central notion in the study of complex networks (see also ).
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  (see also  for a proceeding version of this paper), the model is deﬁned for a variety of metric spaces S.
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