Simon model

In applied probability theory, the Simon model is a class of that results in a power-law distribution function. It was proposed by Herbert A. Simon 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 ${\displaystyle k}$). 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.

To model this type of network growth as described above, Bornholdt and Ebel considered a network with ${\displaystyle n}$ nodes, and each node with connectivities ${\displaystyle k_{i}}$, ${\displaystyle i=1,\ldots ,n}$. These nodes form classes ${\displaystyle [k]}$ of ${\displaystyle f(k)}$ nodes with identical connectivity ${\displaystyle k}$. Repeat the following steps:

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