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Network Rewiring in the r-K Plane.

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  • 1Faculty of Science and Technology, Free University of Bozen-Bolzano, 39100 Bolzano, Italy.

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Summary

Researchers developed a novel rewiring algorithm to control network properties like assortativity and nearest neighbor degree in scale-free networks. This method allows fine-tuning network structure and exploring extreme assortative and disassortative configurations.

Keywords:
network assortativitynetwork entropynetwork rewiringscale-free networks

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Scale-free networks are ubiquitous in nature and technology.
  • Network correlations, such as assortativity and nearest neighbor degree, significantly impact network properties.
  • Controlling these correlations in network models is crucial for understanding and designing complex systems.

Purpose of the Study:

  • To introduce a new rewiring algorithm for generating correlated scale-free networks within the configuration model.
  • To enable simultaneous tuning of the Newman assortativity coefficient (r) and the average nearest neighbor degree (K).
  • To explore the limits of network assortativity, including previously unconsidered cases with small minimum degrees.

Main Methods:

  • A novel rewiring algorithm based on the Metropolis acceptance probability, incorporating a variable temperature (T).
  • Calculation of local variations in assortativity (Δr) and nearest neighbor degree (ΔK) at each rewiring step.
  • Analysis of rewiring trajectories in the r-K plane and monitoring of network properties like giant component size and entropy.

Main Results:

  • A general relation between Δr and ΔK was derived, connecting two distinct topological measures.
  • The algorithm successfully generates networks across a wide range of assortativity coefficients (-1 ≤ r ≤ 1) and nearest neighbor degrees (K ≥ 〈k〉).
  • The average number of second neighbors (z̄₂,B) was proven constant for Markovian networks, independent of correlations.

Conclusions:

  • The developed rewiring algorithm provides a powerful tool for constructing and analyzing correlated scale-free networks.
  • The study establishes a fundamental link between network assortativity and nearest neighbor degree.
  • The findings offer new insights into network connectivity and the behavior of complex systems with varying degrees of correlation.