The probability that the hyperbolic random graph is connected Michel Bode Nikolaos Fountoulakis Tobias Muller y March 6, 2014 Abstract This work is a study of a family of random geometric graphs on the hyperbolic plane. We find the rescaling of network parameters that allows to reduce random hyperbolic graphs of arbitrary dimensionality to a single mathematical framework. Google Scholar; Tobias Friedrich and Anton Krohmer. Our results indicate that RHGs exhibit similar topological properties, regardless of the dimensionality of their latent hyperbolic spaces. 60, 2 (2018), 315--355. We also show that these graphs are not asymptotically δ–hyperbolic for any non–negative δ almost surely as n→∞. We generalize random hyperbolic graphs to arbitrary dimensionality. Percolation on planar hyperbolic graphs. On the diameter of hyperbolic random graphs. We present an efficient algorithm for computing distances in hyperbolic grids. ∙ 0 ∙ share . Our generator can also be … A graph G is transitive if the auto­ morphism group of G acts transitively on the vertices V(G). We further show that when 0 ≤ γ3andd = 1, the random graphs are not polylogarithmically hyperbolic. Hyperbolic grids and discrete random graphs. Introduction to Random Graphs. Configuring random graph models with fixed degree sequences. We apply this algorithm to work efficiently with a discrete variant of the hyperbolic random graph model. Random hyperbolic graphs (RHGs): Introduction I Introduced by Krioukov, Papadopoulos, Kitsak, Vahdat, Boguna˜ [Phys. We propose HyGen, a random graph generator that leverages the recent research on non-clique-like communities to produce realistic random graphs with hyperbolic community structure, degree distribution, and clustering coefficient. On the giant component of random hyperbolic graphs. Welcome to the Hyperbolic Graph Generator Pages. SIAM Rev. 3. Rev. 07/04/2017 ∙ by Eryk Kopczyński, et al. SIAM J. Discr. Bode, M., Fountoulakis, N., Müller, T.: The probability that the hyperbolic random graph is connected (2014). Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. 2015. 2018. ComputerPhysicsCommunications ( ) – Contents lists available atScienceDirect ComputerPhysicsCommunications journal homepage:www.elsevier.com/locate/cpc We showed that the diameter of a hyperbolic random graph is poly-logarithmic with high probability. This software implements and extends the network model described in Hyperbolic Geometry of Complex Networks.Embedded in the hyperbolic plane, these networks naturally exhibit two common properties of real-world networks, namely power-law node degree distribution and strong clustering. Math. cally hyperbolic. In: 7th European Conference on Combinatorics, Graph Theory and Applications (EuroComb), pp. ’10] I Appeal: Replicate characteristic properties observed in “real world networks” or “complex networks” Example of networks: Power grid Internet … 425–429 (2013) Google Scholar. In this paper we prove that random d–regular graphs with d≥3 have traffic congestion of the order O(nlog3d−1(n)) where n is the number of nodes and geodesic routing is used. Although there still exists a gap between hyperbolic δ and graph diameter at the sweet spot of γ = d, our results already Google Scholar; Alan Frieze and Michał Karoński. 32, 2 (2018), 1314--1334. An invariant percola­ tion on a graph G is a probability measure on the space of subgraphs of G, which is invariant under the automorphisms of G. The connected components of the random In this setting, N points are chosen randomly on the hyperbolic plane and any two of

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