By David F. Gleich, Júlia Komjáthy, Nelly Litvak

ISBN-10: 3319267833

ISBN-13: 9783319267838

ISBN-10: 3319267841

ISBN-13: 9783319267845

This e-book constitutes the lawsuits of the twelfth foreign Workshop on Algorithms and versions for the internet Graph, WAW 2015, held in Eindhoven, The Netherlands, in December 2015.

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

**Read or Download Algorithms and Models for the Web Graph: 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015, Proceedings PDF**

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**Additional info for Algorithms and Models for the Web Graph: 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015, Proceedings**

**Sample text**

The proof of Lemma 8 can be found in the full version of this paper [11]. α+c and λ be a constant bigger Lemma 8. Let c ≥ 1 be a constant, Δ := 2 α−1 Δ+2 Δ than max{2e γ Δβ, c}. For G = G(n, m, p) and for all > 0 it holds with 2 probability O(n−c ) that |V (G)|−1 · |{v ∈ V (G) : deg(v) ≥ 2λΔ }| ≤ . α+c Lemma 9. Let c ≥ 1 be a constant, Δ := 2 α−1 , Δ2 := Δ 2 , φ be defined as in Δ+1 Δ 2 Theorem 4 and δr > (2r + 1) · max{e γ ΔΔ β, (c + 1)Δ2 }. Then for every + −3 r ∈ N , for every 0 < < e , and for every H ⊆ G = G(n, m, p) with |H| < n it holds with probability O(n−c ) that ∇r (H) ≥ δr .

Then for every k1 , k2 ≥ 0 we have p(k1 , k2 ) = p∞ (k1 , k2 ) + o(1). (11) We note that the moment conditions < ∞ and EY1 < ∞ of Theorem 3 are the minimal ones as a2 = EX12 and b1 = EY1 enter the expressions deﬁning the quantities on the right side of (10) and (11). EX12 Remark 2. , P(d(v1 ) = r|v1 ∼ v2 ) = p˜(r) + o(1), r = 1, 2, . . (12) Degree-Degree Distribution in a Power Law Random Intersection Graph 47 Our ﬁnal remark is about the case where m/n → 0. By Theorem 1, in this case the edges of a sparse inhomogeneous random intersection graph span a subgraph on o(n) randomly selected vertices leaving the remaining (1 − o(1))n vertices isolated.

D. Sullivan supported in part by DARPA GRAPHS/SPAWAR Grant N66001-141-4063, the Gordon & Betty Moore Foundation, and the National Consortium for Data Science. Any opinions, ﬁndings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reﬂect the views of DARPA, SSC Paciﬁc, DOE, the Moore Foundation, or the NCDS. References 1. : Epidemics on random intersection graphs. Ann. Appl. Probab. 24(3), 1081–1128 (2014) 2. : On the complexity of the herding attack and some related attacks on hash functions.

### Algorithms and Models for the Web Graph: 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015, Proceedings by David F. Gleich, Júlia Komjáthy, Nelly Litvak

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