Correlations in scale-free networks: tomography and percolation

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Scale-free networks are crucial in modeling complex systems.
• The Barabási-Albert model is a foundational scale-free network model.
• Network properties like degree distribution and correlations influence network behavior.

Purpose of the Study:

• To investigate three related scale-free network models with identical degree distributions but varying correlation properties.
• To compare the assortative/disassortative mixing and percolation properties of these models.
• To understand how network randomization affects correlation and percolation behaviors.

Main Methods:

• Utilized the Barabási-Albert model as a base.
• Introduced two network models by randomizing the Barabási-Albert model concerning links and nodes.
• Analyzed degree correlations (assortativity/disassortativity) and network percolation properties.
• Visualized correlation structures using the shell model.

Main Results:

• The Barabási-Albert model exhibits dissortative degree mixing.
• The node-randomized network demonstrates assortative degree mixing.
• Despite differing correlation behaviors, all three network models show similar percolation properties.
• Similar percolation behavior was observed in a network with a finite second moment and its randomized counterparts.

Conclusions:

• Network correlation properties (assortativity/disassortativity) do not significantly alter percolation thresholds in these scale-free models.
• Randomization techniques can tune correlation properties while maintaining similar macroscopic behaviors like percolation.
• The findings contribute to understanding the robustness and resilience of complex networks.