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.
| Original language | English |
|---|---|
| Pages (from-to) | 609-630 |
| Number of pages | 22 |
| Journal | Journal of Applied Probability |
| Volume | 59 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2022 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- Barabási-Albert model
- Bianconi-Barabási model
- Bose-Einstein condensation
- majorization
- orderings
- Preferential attachment with fitness