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On September 20, 2018, Xinwei Bai will defend her PhD thesis "Performance Bounds for Random Walks in the Positive Orthant" at 14:30. Prior to this ceremony, a mini-symposium is held starting at 10:30. We cordially invite you to attend both the symposium and the PhD defense. The event will be held at the University of Twente.
Mini-Symposium on Performance Analysis of Markov Processes
Date: September 20, 2018
Location: Ravelijn 2503
Lunch: Ravelijn Atrium
For more info, see here.
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Speaker: Pim van der Hoorn
Affiliation: Northeastern University, Boston, USA
Titel: Local clustering for graphs in Hyperbolic space
Abstract: Clustering is an important property that is prominently featured in many real-world networks. It has however proven to be a challenge to create random graph models that join this feature with another important property, scale-free degree distributions. One of the first to do this is the Hyperbolic Random Graph model developed by Krioukov et al, where points are sprinkled, uniformly at random, on a hyperbolic disc and two points are connected if their hyperbolic distance is less than a given threshold. The success of this model not only comes from the fact that it combines scale-free degree distribution and non-vanishing clustering. It also enables efficient routing algorithms for networks, based on local information. Due to these features, it has attracted increasing interest from the complex network community. Many structural properties, such as degree distribution, size of the largest component and scaling of clique sizes, have been analyzed. However, for clustering we only know that the global clustering coefficient converges to some constant, which we do not know. In addition, no results are known for the more important local clustering function, which gives for any degree value k the average fraction of triangles in which nodes of degree k participate.
In this talk I will focus on the analysis of the local clustering function in the Hyperbolic Random Graph. In particular, on its asymptotic behavior as the degree value k tends to infinity with the size of the graph. I will show that this scaling undergoes a phase-transition, depending on the exponent of the degree distribution. These results resolve an open conjecture by Krioukov et al. who thought the scaling was always 1/k. This work is part of a larger endeavor, where we also derive complete expressions for the global clustering coefficient and the local clustering function for fixed values of k.
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