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Simon model
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Simon model : ウィキペディア英語版
Simon model
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 k). 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 n nodes, and each node with connectivities k_i, i = 1, \ldots, n. These nodes
form classes () of f(k) nodes with identical connectivity k.
Repeat the following steps:
(i) With probability \alpha add a new node and attach a link to it from an arbitrarily chosen node.
(ii) With probability 1-\alpha add one link from an arbitrary node to a node j of class () chosen with a probability proportional to k f(k).
For this stochastic process, Simon found a stationary solution exhibiting power-law scaling, P(k) \propto k^, with exponent \gamma = 1 + \frac.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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