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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク giant component ： ウィキペディア英語版 giant component In network theory, a giant component is a connected component of a given random graph that contains a constant fraction of the entire graph's vertices. Giant components are a prominent feature of the Erdős–Rényi model of random graphs, in which each possible edge connecting pairs of a given set of vertices is present, independently of the other edges, with probability . In this model, if $p\; \backslash le\; \backslash frac$ for any constant $\backslash epsilon>0$, then with high probability all connected components of the graph have size , and there is no giant component. However, for $p\; \backslash ge\; \backslash frac$ there is with high probability a single giant component, with all other components having size . For $p\; =\; \backslash frac$, intermediate between these two possibilities, the number of vertices in the largest component of the graph is with high probability proportional to $n^$.〔.〕 Alternatively, if one adds randomly selected edges one at a time, starting with an empty graph, then it is not until approximately $n/2$ edges have been added that the graph contains a large component, and soon after that the component becomes giant. More precisely, when $t$ edges have been added, for values of $t$ close to but larger than $n/2$, the size of the giant component is approximately $4t-2n$.〔 However, according to the coupon collector's problem, $\backslash Theta(n\backslash log\; n)$ edges are needed in order to have high probability that the whole random graph is connected. A similar sharp threshold between parameters that lead to graphs with all components small and parameters that lead to a giant component also occurs in random graphs with non-uniform degree distributions.〔.〕 ==References== 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「giant component」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.