翻訳と辞書 |
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 for any constant , then with high probability all connected components of the graph have size , and there is no giant component. However, for there is with high probability a single giant component, with all other components having size . For , intermediate between these two possibilities, the number of vertices in the largest component of the graph is with high probability proportional to .〔.〕 Alternatively, if one adds randomly selected edges one at a time, starting with an empty graph, then it is not until approximately edges have been added that the graph contains a large component, and soon after that the component becomes giant. More precisely, when edges have been added, for values of close to but larger than , the size of the giant component is approximately .〔 However, according to the coupon collector's problem, 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.
|
|