How breadth of degree distribution influences network robustness: comparing localized and random attacks.

Area of Science:

• Network science
• Statistical physics

Background:

• Network stability is significantly affected by degree distribution breadth.
• Broader degree distributions enhance robustness against random failures but decrease it against localized attacks.

Purpose of the Study:

• To investigate the impact of degree distribution breadth on network robustness.
• To compare network vulnerability under localized attacks (LA) versus random attacks (RA).

Main Methods:

• Analytical study and numerical simulations of networks with controlled degree distribution breadth.
• Examination of bi-Poisson and Gaussian degree distributions.
• Analysis of interdependent networks.

Main Results:

• Localized attacks (LA) and random attacks (RA) are equivalent only for pure Poisson distributions (α=0 or α=1).
• Networks are generally more vulnerable to LA than RA, except for pure Poisson distributions.
• For Gaussian distributions, vulnerability depends on the relationship between variance (σ²) and mean degree (μ): σ² < μ implies higher vulnerability to RA, while σ² > μ implies higher vulnerability to LA.

Conclusions:

• Degree distribution breadth critically influences network robustness to different attack types.
• The specific distribution (bi-Poisson, Gaussian) and its parameters dictate the nature and extent of vulnerability.
• Findings extend to interdependent networks, highlighting the importance of distribution tailoring for network resilience.