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

Part of: Distribution theory - Probability Graph theory

Published online by Cambridge University Press:  21 June 2022

Alessandra Cipriani Open the ORCID record for Alessandra Cipriani [Opens in a new window]  and
Andrea Fontanari
Alessandra Cipriani*
Affiliation:
TU Delft
Andrea Fontanari*
Affiliation:
CWI, TU Delft
*
*Postal address: TU Delft (DIAM), Building 28, van Mourik Broekmanweg 6, 2628 XE, Delft, The Netherlands.
*Postal address: TU Delft (DIAM), Building 28, van Mourik Broekmanweg 6, 2628 XE, Delft, The Netherlands.
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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–Barabási and Barabási–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.

Keywords

Preferential attachment with fitnessBarabási–Albert modelBianconi–Barabási modelmajorizationorderingsBose–Einstein condensation

MSC classification

Primary: 05C80: Random graphs
Secondary: 60E15: Inequalities; stochastic orderings
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 3 , September 2022 , pp. 609 - 630
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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