The European Physical Journal Special Topics

, Volume 225, Issue 10, pp 1879–1891 | Cite as

Discretized kinetic theory on scale-free networks

  • Maria Letizia Bertotti
  • Giovanni ModaneseEmail author
Regular Article Theory
Part of the following topical collections:
  1. Complex, Inter-networked Economic and Social Systems


The network of interpersonal connections is one of the possible heterogeneous factors which affect the income distribution emerging from micro-to-macro economic models. In this paper we equip our model discussed in [1, 2] with a network structure. The model is based on a system of n differential equations of the kinetic discretized-Boltzmann kind. The network structure is incorporated in a probabilistic way, through the introduction of a link density P(α) and of correlation coefficients P(β|α), which give the conditioned probability that an individual with α links is connected to one with β links. We study the properties of the equations and give analytical results concerning the existence, normalization and positivity of the solutions. For a fixed network with P(α) = c q , we investigate numerically the dependence of the detailed and marginal equilibrium distributions on the initial conditions and on the exponent q. Our results are compatible with those obtained from the Bouchaud-Mezard model and from agent-based simulations, and provide additional information about the dependence of the individual income on the level of connectivity.


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© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Faculty of Science and Technology, Free University of Bozen-BolzanoBolzanoItaly

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