Emergency of Tsallis statistics in fractal networks

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, o...

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Bibliographic Details
Published in:PloS one 2021-09, Vol.16 (9), p.e0257855-e0257855
Main Authors: Deppman, Airton, Andrade-II, Evandro Oliveira
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Computer and Information Sciences
Ecology and Environmental Sciences
Evaluation
Exponential functions
Fractals
Information management
Information processing
Medicine and Health Sciences
Methods
Networks
Neural networks
Optimization
Physical Sciences
Scale invariance
Statistics
Symmetry
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Summary:Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0257855