Probabilistic prediction in scale-free networks: diameter changes.

Area of Science:

• Complex Systems Science
• Network Science
• Statistical Physics

Background:

• Complex systems exhibit unpredictable responses to small perturbations.
• Understanding network robustness is crucial for real-world applications.
• Scale-free networks are common models for complex systems.

Purpose of the Study:

• To investigate the probabilistic prediction of network responses.
• To analyze diameter changes in scale-free networks upon single vertex deletion.
• To determine the robustness and characteristics of these changes.

Main Methods:

• Analysis of diameter changes in various in silico and real-world scale-free networks.
• Statistical analysis of the distribution of diameter changes.
• Identification of the exponent (zeta) in the algebraic decay of change distribution.

Main Results:

• Diameter changes in scale-free networks are diverse and follow an algebraic decay.
• The decay exponent (zeta) is approximately 2.2(1) for most scale-free networks.
• A distinct network type, including the Internet, shows zeta approximately 1.7(1).

Conclusions:

• The probabilistic approach effectively predicts diverse network responses.
• Scale-free network diameter changes exhibit a robust, predictable decay pattern.
• Network topology influences the specific decay exponent, highlighting distinct network behaviors.