A comprehensive approach for discrete resilience of complex networks

Area of Science:

• Complex Systems Science
• Network Science
• Mathematical Modeling

Background:

• The concept of resilience is widely used across technological, physiological, and socioeconomic systems.
• Existing definitions of resilience vary, often focusing on recovery from failures.
• A unified quantitative approach is needed for comparing resilience across different system types.

Purpose of the Study:

• To establish a theoretical and mathematical framework for discrete resilience.
• To enable quantitative comparison of resilience in diverse systems.
• To provide a definition and local view of resilience for complex networks.

Main Methods:

• Development of a theoretical framework for discrete resilience.
• Formulation of a mathematical model for quantitative resilience assessment.
• Computational experiments on synthetic and real-world networks.

Main Results:

• A novel framework for quantifying discrete resilience is established.
• A local view of resilience applicable to complex network measures is defined.
• The new resilience parameter was evaluated across various network types.

Conclusions:

• The proposed framework offers a quantitative method for assessing discrete resilience.
• This research provides new conceptual tools for network science.
• The findings facilitate cross-system comparisons of resilience and failure recovery.