Abstract
Abstract In this Letter we investigate a connection between Kaniadakis power-law statistics and networks. By following the maximum entropy principle, we maximize the Kaniadakis entropy and derive the optimal degree distribution of complex networks. We show that the degree distribution follows P ( k ) = P 0 exp κ ( − k / η κ ) with exp κ ( x ) = ( 1 + κ 2 x 2 + κ x ) 1 / κ , and | κ | 1 . In order to check our approach we study a preferential attachment growth model introduced by Soares et al. [Europhys. Lett. 70 (2005) 70] and a growing random network (GRN) model investigated by Krapivsky et al. [Phys. Rev. Lett. 85 (2000) 4629]. Our results are compared with the ones calculated through the Tsallis statistics.
Highlights
Over the last years, a lot of effort has been dedicated to studies of networks
In order to check our approach we study a preferential attachment growth model introduced by Soares et al [Europhys
A growing random network (GRN) model investigated by Krapivsky et al [Phys
Summary
A lot of effort has been dedicated to studies of networks. In this concern, a network can be defined as a mathematical abstraction created to represent a relationship between objects. Several consequences (in different branches) of the former framework have been investigated in the literature [8], which include the study of Tsallis statistics in the context of complex networks [9,10,11] In this concern, the Thurner–Tsallis model [9] shows that growth is not necessary for having scale-free degree distributions. Where ηq > 0 defines the characteristics number of links, k is the connectivity and the q-exponential function is defined as expq (x) ≡ 1 + (1 − q)x This new degree distribution, based on the Kaniadakis framework, is the power law that generalizes the exponential distribution.
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