Dynamical fitness models: evidence of universality classes for preferential attachment graphs

Alessandra Cipriani; Andrea Fontanari

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arXiv · 1911.12402

Dynamical fitness models: evidence of universality classes for preferential attachment graphs

Alessandra Cipriani·Andrea Fontanari

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Abstract

In this paper we define a family of preferential attachment models for random graphs with fitness in the following way: independently for each node, at each time step a random fitness is drawn according to the position of a moving average process with positive increments. We will define two regimes in which our graph reproduces some features of two well known preferential attachment models: the Bianconi-Barab\'asi and the Barab\'asi-Albert models. We will discuss a few conjectures on these models, including the convergence of the degree sequence and the appearance of Bose-Einstein condensation in the network when the drift of the fitness process has order comparable to the graph size.

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math.PR cs.SI physics.soc-ph

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BibTeX RIS

Alessandra Cipriani, Andrea Fontanari. 2019-11-27. Dynamical fitness models: evidence of universality classes for preferential attachment graphs. https://arxiv.org/abs/1911.12402

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