By David F. Gleich, Júlia Komjáthy, Nelly Litvak

ISBN-10: 3319267833

ISBN-13: 9783319267838

ISBN-10: 3319267841

ISBN-13: 9783319267845

This ebook constitutes the court cases of the twelfth foreign Workshop on Algorithms and types for the internet Graph, WAW 2015, held in Eindhoven, The Netherlands, in December 2015.

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

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

**Sample text**

Let m, n → +∞. (i) Assume that EX12 < ∞. Let κ > 2 and assume that Y1 ∈ Pc,κ . Suppose that m/n → +∞. Then for k1 , k2 → +∞ we have p(k1 , k2 ) = (1 + o(1))c2 a2κ−4 b2κ−6 (k1 k2 )1−κ . 2 1 (6) (ii) Let a, β > 0 and κ > 3. Assume that EeaY1 < ∞ and X1 ∈ Pc,κ . Suppose that m/n → β. Let k1 , k2 → +∞ so that k1 ≤ k2 . Suppose that either k2 − k1 → +∞ or k2 − k1 = k, for an arbitrary, but fixed integer k ≥ 0. Then p(k1 , k2 ) = (1 + o(1)) β ∗ c f (k1 , k2 ), b41 a2 1 (7) where f (k1 , k2 ) = c∗2 k12−κ (k2 − k1 )1−κ , f (k1 , k2 ) = c∗3,k k12−κ , for k2 − k1 → +∞, for k2 − k1 = k.

Suppose that m/n → +∞. Then for k1 , k2 → +∞ we have p(k1 , k2 ) = (1 + o(1))c2 a2κ−4 b2κ−6 (k1 k2 )1−κ . 2 1 (6) (ii) Let a, β > 0 and κ > 3. Assume that EeaY1 < ∞ and X1 ∈ Pc,κ . Suppose that m/n → β. Let k1 , k2 → +∞ so that k1 ≤ k2 . Suppose that either k2 − k1 → +∞ or k2 − k1 = k, for an arbitrary, but fixed integer k ≥ 0. Then p(k1 , k2 ) = (1 + o(1)) β ∗ c f (k1 , k2 ), b41 a2 1 (7) where f (k1 , k2 ) = c∗2 k12−κ (k2 − k1 )1−κ , f (k1 , k2 ) = c∗3,k k12−κ , for k2 − k1 → +∞, for k2 − k1 = k.

4) P(Λ3 = r) = Ee−λ3 3 , r! Here λ3 = Y1 a2 b1 . (iii) Assume that m/n → 0. Suppose that EX1 < ∞. Then P(d(v1 ) = 0) = 1 − o(1). Using the fact that a Poisson random variable is highly concentrated around its mean one can show that for a power law distribution P(λi > r) ∼ ci r−κi , with some ci , κi > 0, we have P(Λi > r) ∼ ci r−κi , for i = 0, 1, 3. Here and below for real sequences {tr }r≥1 and {sr }r≥1 we denote tr ∼ sr whenever tr /sr → 1 as r → +∞. , [1]. Hence, choosing a power law weights X and Y we obtain a power law asymptotic degree distributions, namely, the distributions of d∗ and Λ3 .

### 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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