By David F. Gleich, Júlia Komjáthy, Nelly Litvak
This e-book constitutes the court cases 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 rigorously reviewed and chosen from 24 submissions. they're equipped in topical sections named: houses of huge graph types, dynamic procedures 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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Extra info for Algorithms and Models for the Web Graph: 12th International Workshop, WAW 2015, Eindhoven, The Netherlands, December 10-11, 2015, Proceedings
Formally, the density of every minor of G is bounded by a function of the depth of that minor (the maximum radius of its branch sets). Bounded expansion oﬀers a structural generalization of both bounded-degree and graphs excluding a (topological) minor. Algorithmically, this property is 1 Not related to the notion of expander graphs. F. Gleich et al. ): WAW 2015, LNCS 9479, pp. 29–41, 2015. 1007/978-3-319-26784-5 3 30 M. Farrell et al. extremely useful: every ﬁrst-order-deﬁnable problem is decidable in linear fpttime in these classes .
Despite the fact that the T-subclass generalizes many diﬀerent models, we are able to analyze the local clustering coeﬃcient for all these models. Namely, we proved that C(d) 2D · d−1 . In particular, this result implies that one asymptotically decreases as Am cannot change the exponent −1 by varying the parameters A, D, and m. This basically means that preferential attachment models in general are not ﬂexible enough to model C(d) ∼ d−ψ with ψ = 1. We would also like to mention the connection between the obtained result and the notion of weak and strong transitivity introduced in .
2 It should be noted that constant clustering and bounded expansion are not orthogonal . 32 M. Farrell et al. We note that G(n, m, p) deﬁnes a distribution Gn on graphs with n vertices. The notation G = G(n, m, p) denotes a graph G that is randomly sampled from the distribution Gn . Throughout the manuscript, given a random intersection graph G(n, m, p) we will refer to B, the associated bipartite graph on n nodes and m attributes from which G is formed. In order to work with graph classes formed by the random intersection graph model, we will need a technical result that bounds the number of attributes in the neighborhood of a subset of nodes around its expected value.