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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 Local World Evolving Network Models ： ウィキペディア英語版 Local World Evolving Network Models Evolving networks are dynamic networks which change in time. In each period t there are new nodes and edges that join the network while the old ones disappear. Such dynamic behaviour is characteristic for most real-world networks, regardless of their range - global or local. However, networks differ not only in their range but also in their topological structure. It is possible to distinguish: * Random networks * Free- scale networks * Small - world networks * Local – world networks One of the main feature which allows to differentiate networks is their evolution process. In random networks points are added and removed from the network in a totally random way (model of Erdős and Rényi).〔Erdős,P. and A.Rényi (1961). On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci,Vol.5, p.17-61〕 Evolution of free scale networks is based on the preferential attachment – nodes connect to nodes that have already possessed a large number of links. In result hubs (nodes that have the largest number of edges) are created and networks follow power law of distribution (model of Barabási and Albert's〔Albert, R. and A.L.Barabasi (2000). Physical Review Letters, Vol.85, No.24, p.5234〕). In opposite, in small world networks there are no hubs, and nodes are rather egalitarian and locally grouped in smaller clusters. These kind of networks are described by Watts and Strogatz (WS) model.〔Watts,J.D. and H.S.Strogatz (1998). Collective dynamics of 'small-world' networks, Nature, Vol.393, p.440-442〕 All aforementioned models assume that newly added points have a global information about the whole network. However, in case of large systems, such knowledge is rather rare. This strongly limits nodes’ possibilities of connection choice. As a result, decisions about links are made rather in a local world than in the whole network. Networks which consider this locality are called local-world networks and were first described by the Li and Chen model (2003). The local world model was extended inter alia by Gardeñes and Moreno (2004), Sen and Zhong,〔Sen,Q. and D.G.Zhong ()Chinese Physics B, Vol.18, No.2, p.383〕 Wen et al.〔Wen,G., Z.Duan, G.Chen G and X.Geng (2011). Physica A, Vol.390, p.4012〕 or Xuan et al.〔Xuan,Q., Y.Li and T.Wu (2007). Physica A, Vol.378, p.561〕 == World Evolving Network Model of Li and Chen (2003) == The model starts with the set of small number of nodes $m\_$ and the small number of edges $e\_$. There are M nodes that were selected randomly from the whole global network, so that they constitute a so-called “local world” for new coming nodes. Thus, every new node with m edges connects only to m existing nodes from its local world and does not link with nodes which are in the global system (the main difference from the BA model). In such case, the probability of connection may be defined as: : $P\_^(k\_)=P^(i\backslash in\; Local-World)\backslash frack\_^$ Where  $P^(i\backslash in\; Local-World)=\backslash frac\}$ and the term "Local-World" refers to all nodes, which are in interest of newly added node at time t. Thus, it may be rewritten: : $P\_^(k\_)=\backslash frac+t\}\backslash frack\_^$ while the dynamics are: : $\backslash frac=\backslash frac+t\}\backslash frack\_^$ In every time ''t'', it is true that  $m\backslash leqslant\; M\backslash leqslant\; m\_+t$, so that two corner solutions are possible:  $M=m$ and  $M=m\_+t$. 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「Local World Evolving Network Models」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.