“Dynamical fitness models: evidence of universality classes for preferential attachment”
Venerdì 31 Gennaio 2020, ore 11:30 - Aula 1BC45 - Alessandra Cipriani (TU Delft)
In this talk we study different variations of a particular class of random graphs called preferential attachment models with fitness. These are dynamic graphs in which, at every time step, a new node attaches itself to an older one with probability proportional to the degree and a random factor associated to the node, called the fitness. Motivated by learning mechanisms of real-life networks, we assume the fitness to be a Moving Average process MA(q) with positive increments. We study different properties of such models, for example the degree distribution, the attachment probability and the phenomenon of Bose-Einstein condensation. Finally we provide evidence that, tuning the parameters of the fitness process, we fall into two universality classes represented by the well-known Albert-Barabàsi model and Bianconi-Barabàsi model. This implies the robustness of heavy tails in the degree distribution under random perturbations of the attachment rule.