Unveiling robustness and heterogeneity through percolation triggered by random-link breakdown.

Area of Science:

• Network Science
• Complex Systems Analysis
• Statistical Physics

Background:

• Heterogeneously connected networks exhibit known robustness to random failures and vulnerability to targeted attacks.
• Quantifying network heterogeneity for robustness remains an underexplored area in complex network research.

Purpose of the Study:

• To propose novel percolation models for assessing network robustness against random link errors.
• To develop dynamic measures for quantifying network heterogeneity based on observed resilience behaviors.

Main Methods:

• Introduced two percolation models on general networks triggered by random link errors.
• Analyzed percolation thresholds and the fraction of the giant cluster to observe resilience.
• Defined compact measures of network heterogeneity by comparing discrepancies between the two models.

Main Results:

• Observed rich resilience behaviors in complex networks, including variations in percolation thresholds and giant cluster fractions.
• Identified discrepancies between the two proposed percolation models.
• Developed new, discriminative measures for quantifying network heterogeneity.

Conclusions:

• The proposed percolation models and heterogeneity measures offer insights into the resilience of complex networks.
• Established a link between network performance, structural properties, and dynamic behaviors.
• Provided a framework for understanding how network heterogeneity impacts robustness against random errors.