Random geometric graphs on the hyperbolic plane
Random graphs on the hyperbolic plane
... Euclidean random geometric graphs naturally exhibit clustering. However, they cannot both have the small world phenomenon and sparseness. This is essentially caused by the fact that in euclidean ...
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Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs
... the hyperbolic random graph (HRG) model ...at random from a disk in the hyperbolic ...the geometric inhomogeneous random graph (GIRG) model ...
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Geometric Inhomogeneous Random Graphs
... a random graph from a fixed distribution, are known for Chung-Lu random graphs and others, running in expected linear time [4, ...threshold hyperbolic random graphs with expected ...
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Hyperbolic Random Graphs: Separators and Treewidth
... degree-distribution, hyperbolic random graphs exhibit other prop- erties of large real-world ...the geometric notion of closeness, vertices with a common neighbor are likely also connected, ...
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A Bound for the Diameter of Random Hyperbolic Graphs
... of hyperbolic space, either by providing useful approximations for the angles formed by two adjacent sides of a triangle whose vertices are at given distances, or by establishing good approximations for the mass ...
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CiteSeerX — Synchronization in Random Geometric Graphs
... typical random networks, namely their clustering coefficent hCi and the average path length ...in random ER networks with the same number of nodes, N, and links, N l ...ER graphs with the same N and ...
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HyGen: generating random graphs with hyperbolic communities
... time-evolving hyperbolic communities, even though there are some important future directions to ...at random; potentially more realistic model would depend, for instance, on the length of the node’s ...
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On the second largest component of random hyperbolic graphs
... enyi random graph model. For the random hyperbolic graph model, the study of the largest component’s size was started by Bode, Fountoulakis and M¨ uller [BFM13] and recently refined by Foun- toulakis ...
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On the Normalized Laplacian Spectra of Random Geometric Graphs
... of random matrices such as adjacency matri- ces, transition probability matrices and normalized ...those random matrices are fundamental tools to predict and analyze complex net- works ...
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Chasing robbers on percolated random geometric graphs
... Thus, each of our three teams can indeed prevent the robber from crossing a chosen path (after an initiation phase). What is more, the robber can never get to within distance 0.99r of any vertex of such a path. We can ...
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Bootstrap Percolation on Geometric Inhomogeneous Random Graphs
... Chung-Lu graphs, where the expected number of initially infected vertices must be polynomial in n (if the set of initially infected vertices is chosen at ...the random graphs is sufficiently strong ...
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On the distance-profile of random rooted plane graphs
... dark) such that each light (resp. dark) face is adjacent only to dark (resp. light) faces. By convention (since there are exactly two possible colorings), the root face is dark. As shown in Bernardi et al. (2014), there ...
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Spectral Gap of Random Hyperbolic Graphs and Related Parameters
... random graphs exhibiting either scale freeness or non-vanishing clustering coefficient have been ...as random hyperbolic graph model, which is a variant of the classical random ...
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Phase transitions for random geometric preferential attachment graphs
... the geometric component is weak, the limiting degree sequence mimics the standard Barab´ asi–Albert preferential attachment ...strong geometric component, the limiting degree sequence mimics a purely ...
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Probabilistic analysis of highly connected random geometric graphs
... One of the reasons to prove our functionals have these properties is to use partitioning algo- rithms that rapidly compute near-optimal solutions on typical examples. To explain this perfor- mance, we apply smoothed ...
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Coloring Kk-free intersection graphs of geometric objects in the plane
... topological graphs We next discuss a few applications of the above results to graph drawings, beginning with some pertinent ...the plane so that its vertices are represented by points and its edges are ...
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Solving Vertex Cover in Polynomial Time on Hyperbolic Random Graphs
... The proof of Theorem 2 consists of two parts that make use of the underlying hyperbolic geometry. In the first part, we show that applying the dominance reduction rule once removes all vertices in the inner part ...
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Corrected mean-field model for random sequential adsorption on random geometric graphs
... clustered random graph model with tunable local clustering and a sparse superimposed ...the random geometric ...tractable random network model and the intractable random ...
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The Hyperbolic Number Plane
... its hyperbolic length in ...the hyperbolic distance under change of orthogonal coordinates in the Lorentz plane is seen to be a geometric expression of the relativity of physical length ...
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Performance Testing of RNSC and MCL Algorithms on Random Geometric Graphs
... bork2455 graph. For the real test graph, RNSC is performing better in producing clusters compared to MCL. It is obvious that RNSC is more optimal compared to MCL. Fig 6 shows the visual representation of real RGG ...
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