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 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
Contents
Description
To model this type of network growth as described above, Bornholdt and Ebel considered a network with
(i) With probability
(ii) With probability
For this stochastic process, Simon found a stationary solution exhibiting power-law scaling,
Properties
(i) Barabási-Albert (BA) model can be mapped to the subclass
(ii) The only free parameter of the model
(iii) The interest in the scale-free model comes from its ability to describe the topology of complex networks. The Simon model does not have an underlying network structure, as it was designed to describe events whose frequency follows a power-law. Thus network measures going beyond the degree distribution such as the average path length, spectral properties, and clustering coefficient, cannot be obtained from this mapping.
The Simon model is related to generalized scale-free models with growth and preferential attachment properties. For more reference, see.