Link cascades in complex networks: A mean-field approach

Area of Science:

• Complex Systems Science
• Network Science
• Computational Social Science

Background:

• Cascade models are crucial for understanding system failures, but typically focus on node damage.
• Link damage is a significant factor in real-world networks across various domains like transportation and social dynamics.
• Existing models do not adequately address the impact of link damage on network integrity.

Purpose of the Study:

• To generalize conventional cascade models by incorporating link damage.
• To develop and analyze a novel link cascade model.
• To identify the relationship between node degree and resistance to link damage.

Main Methods:

• Proposed a link cascade model building upon the standard independent cascade model.
• Employed numerical simulation and analytic approximation to solve the model.
• Applied the model to analyze sign distributions in a real-world signed social network.

Main Results:

• The probability of a node losing all links due to damage shows a minimum concerning node degree.
• An optimal node degree exists, conferring maximum resistance to link damage.
• Empirical validation confirmed the existence of this optimal degree in a real-world signed social network.

Conclusions:

• The proposed link cascade model provides a more comprehensive framework for studying network failures.
• Node degree plays a critical role in network resilience against link damage.
• The findings have implications for understanding and designing robust complex systems.