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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 Low-degree saturation ： ウィキペディア英語版 Low-degree saturation In a scale-free network the degree distribution follows a power law function. In some empirical examples this power-law fits the degree distribution well only in the high degree region, however for small degree nodes the empirical degree-distribution deviates from it. See for example the network of scientific citations. This deviation of the observed degree-distribution from the theoretical prediction at the low-degree region is often referred as low-degree saturation.〔(【引用サイトリンク】first1=Albert-László )〕 Typically the empirical degree-distribution deviates downwards from the power-law function fitted on higher order nodes, which means low-degree nodes are less frequent in real data than what is predicted by the Barabási–Albert model. == Theoretical foundation == One of the key assumptions of the BA model is preferential attachment. It states, the probability of acquiring a new link from a new entrant node is proportional to the degree of each node. In other words, every new entrant favors to connect to higher-degree nodes. Formally: $\backslash Pi\backslash left(k\_i\backslash right)=\backslash frac$ Where $\backslash Pi\backslash left(k\_i\backslash right)$ is the probability of acquiring a link by a node with degree $k$. With a slight modification of this rule low-degree saturation can be predicted easily, by adding a term called initial attractiveness ($A$). This was first introduced by Dorogovtsev, Mendes and Samukhin in 2000. $\backslash Pi\backslash left(k\_i\backslash right)=\backslash frac$ With this modified attachment rule a low-degree node (with low $k$) has a higher probability to acquire new links compared to the original set-up. Thus it is more ''attractive''. Therefore, this handicap makes less likely the existence of small degree-nodes as it is observed in real data. More formally this modifies the degree distribution as: $p\_k\; =\; C\backslash left(k\; +\; A\; \backslash right)^$ As a side effect it also increases the exponent relative to the original BA model. It is called ''initial'' attractiveness because in the BA framework every node grows in degree by time. And as $k$ goes large the significance of this fixed additive term $(A)$ diminishes. 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「Low-degree saturation」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.