By David F. Gleich, Júlia Komjáthy, Nelly Litvak

ISBN-10: 3319267833

ISBN-13: 9783319267838

ISBN-10: 3319267841

ISBN-13: 9783319267845

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

The 15 complete papers offered during this quantity have been rigorously reviewed and chosen from 24 submissions. they're geared up in topical sections named: homes of enormous graph versions, dynamic methods 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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Phys. Rev. E 84, 066108 (2011) 19. : Grad and classes with bounded expansion I. and II. Eur. J. Comb. 29(3), 760–791 (2008) 20. : First order properties on nowhere dense structures. J. Symbolic Logic 75(3), 868–887 (2010) 21. : On nowhere dense graphs. Eur. J. Comb. 32(4), 600–617 (2011) 22. : Sparsity: Graphs, Structures, and Algorithms. Algorithms and Combinatorics, vol. 28. Springer, Heidelberg (2012) 23. : Characterisations and examples of graph classes with bounded expansion. Eur. J. Comb.

That is, if G is δ-hyperbolic, then for each triple of vertices x, y, z, and every choice of three shortest paths connecting them pairwise, each point on the shortest path from x to y must be within distance δ of a point on one of the other 34 M. Farrell et al. paths. The hyperbolicity of a graph G is the minimum δ ≥ 0 so that G is δhyperbolic. Note that a trivial upper bound on the hyperbolicity is half the diameter (this is true for any graph). In this paper we give lower bounds for the hyperbolicity of the graphs in G(n, m, p).

Xm , Y1 , . . , Yn be independent non-negative random variables such that each Xi has the probability distribution P1 and each Yj has the probability distribution P2 . Given realized values X = {Xi }m i=1 and Y = {Yj }nj=1 we deﬁne the random bipartite graph HX,Y with the bipartition V ∪ W , where V = {v1 , . . , vn } and W = {w1 , . . , wm }. Every pair {wi , vj } is linked in HX,Y with probability pij = min{1, λij }, where Xi Yj , λij = √ nm independently of the other pairs {w, v} ∈ W × V .

### 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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