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Entropic origin of disassortativity in complex networks
Samuel Johnson1, Joaquín J Torres, J Marro
1Departamento de Electromagnetismo y Física de la Materia, and Institute Carlos I for Theoretical and Computational Physics, Facultad de Ciencias, University of Granada, 18071 Granada, Spain.
Physical Review Letters
|April 7, 2010
Summary
Most empirical networks exhibit degree-degree anticorrelation, except social networks. This study explains this phenomenon using a neutral model for correlated networks, predicting disassortativity in scale-free networks.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Empirical networks often display degree-degree anticorrelation, a pattern not observed in social networks.
- Understanding the underlying mechanisms driving network correlations is a long-standing question in network science.
Purpose of the Study:
- To explain why most empirical networks are degree-degree anticorrelated.
- To provide a neutral model for predicting network correlations in the absence of specific evolutionary information.
Main Methods:
- Definition of the ensemble of correlated networks.
- Calculation of the associated Shannon entropy.
- Analysis of maximum entropy configurations for assortative and disassortative networks.
Main Results:
- Scale-free networks with high heterogeneity are predicted to be disassortative.
- The proposed neutral model yields the expected value of correlations for various network types.
- Social networks deviate from neutral predictions, suggesting specific correlating mechanisms.
Conclusions:
- The generic degree-degree anticorrelation in most empirical networks, particularly scale-free ones, can be explained by a maximum entropy principle.
- Deviations from these neutral predictions, as seen in social networks, highlight the presence of distinct network formation processes.
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