翻訳と辞書 Words near each other ・ Hyperbius ・ HyperBlade ・ Hyperbola ・ Hyperbole ・ Hyperbole and a Half ・ Hyperbolic ・ Hyperbolic 3-manifold ・ Hyperbolic absolute risk aversion ・ Hyperbolic angle ・ Hyperbolic coordinates ・ Hyperbolic Dehn surgery ・ Hyperbolic discounting ・ Hyperbolic distribution ・ Hyperbolic equilibrium point ・ Hyperbolic function ・ Hyperbolic geometric graph ・ Hyperbolic geometry ・ Hyperbolic group ・ Hyperbolic growth ・ Hyperbolic law of cosines ・ Hyperbolic link ・ Hyperbolic manifold ・ Hyperbolic motion ・ Hyperbolic motion (relativity) ・ Hyperbolic navigation ・ Hyperbolic orthogonality ・ Hyperbolic partial differential equation ・ Hyperbolic plane (disambiguation) ・ Hyperbolic point ・ Hyperbolic quaternion Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hyperbolic geometric graph ： ウィキペディア英語版 Hyperbolic geometric graph A hyperbolic geometric graph (HGG) or hyperbolic geometric network (HGN) is special spatial network where nodes are (1) sprinkled according to a probability distribution onto a hyperbolic space of constant negative curvature and (2) an edge between two nodes is present if they are close according to a function of the metric, a HGG generalizes a random geometric graph (RGG) whose embedding space is Euclidean. == Mathematical formulation == Mathematically, a HGG is a graph $G(V,E)$ with a vertex set ''V'' (cardinality $N=|V|$) and a edge set ''E'' constructed by considering the nodes as points placed onto a 2-dimensional hyperbolic space $\backslash mathbb^2\_\backslash zeta$ of constant negative Gaussian curvature, $-\backslash zeta^2$ and cut-off radius $R$, i.e. the radius of the Poincaré disk which can be visualized using a hyperboloid model. Each point $i$ has hyperbolic polar coordinates $(r\_i,\backslash theta\_i)$ with $0\backslash leq\; r\_i\backslash leq\; R$ and . The hyperbolic law of cosines allows to measure the distance $d\_$ between two points $i$ and $j$,〔 :$\backslash cosh(\backslash zeta\; d\_)=\backslash cosh(\backslash zeta\; r\_i)\backslash cosh(\backslash zeta\; r\_j)$$-\backslash sinh(\backslash zeta\; r\_i)\backslash sinh(\backslash zeta\; r\_j)\backslash cos\backslash bigg(\backslash underbrace\_\backslash bigg).$ The angle $\backslash Delta$ is the (smallest) angle between the two position vectors. In the simplest case, an edge $(i,j)$ is established iff (if and only if) two nodes are within a certain ''neighborhood radius'' $r$, $d\_\backslash leq\; r$, this corresponds to an influence threshold. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hyperbolic geometric graph」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.