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By David F. Gleich, Júlia Komjáthy, Nelly Litvak

This publication constitutes the complaints 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: homes of huge graph versions, dynamic methods on huge graphs, and homes of PageRank on huge graphs.

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

This booklet constitutes the lawsuits of the twelfth foreign 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 conscientiously reviewed and chosen from 24 submissions. they're prepared in topical sections named: homes of enormous graph types, dynamic strategies on huge graphs, and houses of PageRank on huge graphs.

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

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Since δr > (c + 1)Δ2 ≥ c/(α − 1), we have: n (2r + 1)rδr k · k=2δr φ n α−1 2 k ≤ ξ (2r + 1)φδr ξ (2r + 1)φδr ≤ = O(n−c ). (6) (α−1)δ r nc n Combining (5) and (6), Eq. (2) is bounded by O(n−c ), as claimed. 4 Hyperbolicity We now turn to the question of whether the structure of the shortest-path distances in random intersection graphs is tree-like (using Gromov’s δ-hyperbolicity as defined in Sect. 3) where we establish a negative result by giving a logarithmic lower bound, for all values of α. The details of the proof can be found in the full version of the paper [11].

General formalism. Phys. Rev. E 74, 056114 (2006) 22. : Clustering in complex networks. II. Percolation properties. Phys. Rev. E 74, 056115 (2006) 23. : Large-scale topological and dynamical properties of the internet. Phys. Rev. E 65, 066130 (2002) 24. : Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998) 25. : Maximal planar networks with large clustering coefficient and power-law degree distribution. Phys. Rev. E 71(4), 046141 (2005) Hyperbolicity, Degeneracy, and Expansion of Random Intersection Graphs Matthew Farrell1 , Timothy D.

Theorem 1. Fix constants α, β and γ. Let m = βnα and p = γn−(1+α)/2 . Let G = G(n, m, p). p. (i) If α < 1, G(n, m, p) is somewhere dense and G has degeneracy Ω(γn(1−α)/2 ). (ii) If α = 1, G(n, m, p) is somewhere dense and G has degeneracy Ω( logloglogn n ). (iii) If α > 1, G(n, m, p) has bounded expansion and thus G has degeneracy O(1). We prove Theorem 1 separately for each of the three ranges of α. 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).

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