A k-deformed Model of Growing Complex Networks with Fitness

Abstract

The Barab\'asi-Bianconi (BB) fitness model can be solved by a mapping between the original network growth model to an idealized bosonic gas. The well-known transition to Bose-Einstein condensation in the latter then corresponds to the emergence of "super-hubs" in the network model. Motivated by the preservation of the scale-free property, thermodynamic stability and self-duality, we generalize the original extensive mapping of the BB fitness model by using the nonextensive Kaniadakis k-distribution. Through numerical simulation and mean-field calculations we show that deviations from extensivity do not compromise qualitative features of the phase transition. Analysis of the critical temperature yields a monotonically decreasing dependence on the nonextensive parameter k.