Preferential urn model and nongrowing complex networks

Abstract

A preferential urn model, which is based on the concept "the rich get richer," is proposed. From a relationship between a nongrowing model for complex networks and the preferential urn model in regard to degree distributions, it is revealed that a fitness parameter in the nongrowing model is interpreted as an inverse local temperature in the preferential urn model. Furthermore, it is clarified that the preferential urn model with randomness generates a fat-tailed occupation distribution; the concept of the local temperature enables us to understand the fat-tailed occupation distribution intuitively. Since the preferential urn model is a simple stochastic model, it can be applied to research on not only the nongrowing complex networks, but also many other fields such as econophysics and social sciences.