A k-deformed Model of Growing Complex Networks with Fitness

Abstract

The Barabási-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.

References in corpus (14)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Power-law distributions in empirical data
• Connectivity of Growing Random Networks
• Bose-Einstein condensation in complex networks
• Statistical mechanics in the context of special relativity
• Maximum entropy principle and power-law tailed distributions
• Non-gaussian statistics and stellar rotational velocities of main sequence field stars
• Kappa-deformed Statistics and the Formation of a Quark-Gluon Plasma
• Bose-Einstein Condensation in the Framework of $\kappa$-Statistics
• Dynamics of condensation in growing complex networks
• On leaders and condensates in a growing network
• Tsallis mapping in growing complex networks with fitness

Cited by in corpus (5)

• The k-statistics approach to epidemiology
• $\kappa$-Deformed quantum and classical mechanics for a system with position-dependent effective mass
• New power-law tailed distributions emerging in $\kappa$-statistics
• Composition law of $\kappa$-entropy for statistically independent systems
• Nonlinear Kinetics on Lattices based on the Kinetic Interaction Principle