Scaled gromov hyperbolic graphs
WebJun 23, 2024 · Gromov Hyperbolic Graphs Arising From Iterations. For a contractive iterated function system (IFS), it is known that there is a natural hyperbolic graph structure … WebPart III deals with large scale Gromov δ-hyperbolic spaces and its mani-festation in many physical and logical network graphs, where the δ-hyperbolic property can be viewed as a formalization of the well known, visually intuitive “core concentric” property. The first chapter introduces the various fatness,
Scaled gromov hyperbolic graphs
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WebApr 14, 2024 · 2.2 Gromov’s \(\delta \)-hyperbolicity. HGCN has shown that the benefits gain of hyperbolic space over Euclidean space is related to the degree of tree-likeness of the graph which can be measured by Gromov’s \(\delta \)-hyperbolicity. Here we take a simple example to describe the definition of \(\delta \)-hyperbolicity. WebOct 12, 2007 · Here the idea is to scale δ relative to the diameter of the geodesic triangles and use the Cartan–Alexandrov–Toponogov (CAT) theory to derive the thresholding value …
Webthe Gromov approach a problem that this paper speciflcally addresses is that the concept of –-hyperbolic geodesic metric spaces hardly makes any sense for flnite graphs, as every flnite graph no matter how awesome its size has flnite –. In a flnite graph, a more relevant measure would be the – of the triangles properly scaled by ... WebJul 20, 2013 · Abstract. We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ 2 with convex tiles is non-hyperbolic; it is shown that in order to ...
Webhyperbolic groups; more generally, the group-theoretic analogues of finite volume com-plete hyperbolic manifolds are relatively hyperbolic groups. The volume growth behaviour of Riemannian balls in the universal covering of a compact Riemannian manifold is the same as the growth behaviour of balls in Cayley graphs of the fundamental group. WebAug 6, 2013 · If G is a graph that is neither a tree nor a unicycle graph, then there exists a 3-regular graph G ′ such that G is hyperbolic if and only if G ′ is hyperbolic. Furthermore, G ′ …
WebJun 5, 2024 · Gromov hyperbolic space. This notion provides a uniform "global" approach to such objects as the hyperbolic plane, simply-connected Riemannian manifolds with …
WebThe hyperbolicity of graphs is typically measured by Gromov’s hyperbolic δ [Gromov 87, Bridson and Haefliger 99] (see Section 2). The hyperbolic δ of a graph measures the “treelikeness” of the graph in terms of the graph distance metric. It can range from 0 to half the graph diameter, with trees having δ =0, the lamb familyWebDec 1, 2016 · The shortest-path distances between the nodes give the natural metric of the graph; hence, it appears that the tree graphs are ideally hyperbolic, i.e. they have the hyperbolicity parameter δ... thwomp from super marioWebThe space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. In this … the lamb gerald coleman lyricsWebIn mathematics, a hyperbolic metric spaceis a metric spacesatisfying certain metric relations (depending quantitatively on a nonnegative real number δ) between points. The … thwompoidWebSep 15, 2005 · Gromov hyperbolic space. Gromov boundary. Quasi-möbius map. 1. IntroductionThe theory of Gromov hyperbolic spaces, introduced by Gromov in the 1980s, … the lamb farnham facebookWebJul 20, 2013 · A weaker version of this conjecture stating that every tessellation graph of ℝ2 with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture … the lamb house hauntingWebAug 6, 2013 · The study of hyperbolic graphs is an interesting topic since, as we have seen, the hyperbolicity of many geodesic metric spaces is equivalent to the hyperbolicity of … thwomp nsmbds