Algorithms and Models for the Web Graph: 12th International by David F. Gleich, Júlia Komjáthy, Nelly Litvak

By David F. Gleich, Júlia Komjáthy, Nelly Litvak

This publication constitutes the complaints of the twelfth overseas Workshop on Algorithms and versions for the net Graph, WAW 2015, held in Eindhoven, The Netherlands, in December 2015.

The 15 complete papers awarded during this quantity have been rigorously reviewed and chosen from 24 submissions. they're equipped in topical sections named: homes of enormous graph types, dynamic approaches on huge graphs, and houses of PageRank on huge graphs.

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Extra info for Algorithms and Models for the Web Graph: 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015, Proceedings (Lecture Notes in Computer Science)

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Statement (i) follows from the relation P(Λ3 = r) ∼ c(a2 b1 )κ−1 r−κ , see Lemma 1. In the proof of (ii) and (iii) we assume that k1 ≤ k2 and use the notation SA = (r + 1)(r + 2)P(Λ0 = r + 2)qk1 −r qk2 −r , A ∈ [0, k1 ]. r∈A Let us prove (ii). We observe that E(eaY1 ) < ∞ implies that EY1 ea Λ1 < ∞ for some a > 0. Using this observation and the fact that the sequence of probabilities {P(τ1 = r)}r≥0 is longtailed and subexponential (see (15) and [9]) we show that (16) E Y1 P(d∗Y1 = r|Y1 ) ∼ E(Y1 Λ1 ) P(τ1 = r).

P. the random intersection graph model generates graph classes with unbounded degeneracy by establishing the existence of a high-degree attribute in the associated bipartite graph (thus lower-bounding the clique number). These proofs can be found in the full version of this paper [11]. In the remainder of this section, we focus on the case when α > 1, as this is the parameter range in which the model generates sparse graphs. Here, we present the general structure of the proof of Theorem 1 for the case α > 1.

Rev. E 64(2), 026118 (2001) 25. : Diameter, connectivity, and phase transition of the uniform random intersection graph. Discrete Math. 311, 1998–2019 (2011) 26. : The coupling method for inhomogeneous random intersection graphs. Preprint. 0466 (2013) 27. : Random intersection graphs. D. thesis, Department of Mathematical Sciences, The Johns Hopkins University (1995) 28. : Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998) 29. : Minimum node degree and k-connectivity in wireless networks with unreliable links.

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