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In applied probability theory, the Simon model is a class of stochastic models that results in a power-law distribution function. It was proposed by Herbert A. Simon〔Simon, H. A., 1955, Biometrika 42, 425.〕 to account for the wide range of empirical distributions following a power-law. It models the dynamics of a system of elements with associated counters (e.g., words and their frequencies in texts, or nodes in a network and their connectivity ). In this model the dynamics of the system is based on constant growth via addition of new elements (new instances of words) as well as incrementing the counters (new occurrences of a word) at a rate proportional to their current values. == Description == To model this type of network growth as described above, Bornholdt and Ebel〔Bornholdt, S. and H. Ebel, Phys. Rev. E 64 (2001) 035104(R).〕 considered a network with nodes, and each node with connectivities , . These nodes form classes of nodes with identical connectivity . Repeat the following steps: (i) With probability add a new node and attach a link to it from an arbitrarily chosen node. (ii) With probability add one link from an arbitrary node to a node of class chosen with a probability proportional to . For this stochastic process, Simon found a stationary solution exhibiting power-law scaling, , with exponent 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「Simon model」の詳細全文を読む スポンサード リンク
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