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Percolation of interdependent networks with intersimilarity.
Yanqing Hu1, Dong Zhou2, Rui Zhang3
1School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China and Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
Summary
Interdependent networks with intersimilarity show reduced cascading failures. This study analytically models this effect, revealing that while cascades decrease with increasing intersimilarity, the phase transition remains discontinuous.
Area of Science:
- Network Science
- Complex Systems
- Statistical Physics
Background:
- Real-world interdependent networks often exhibit intersimilarity, where connected nodes share interdependent neighbors.
- Intersimilarity, measured by common links, is suggested to reduce cascading failures in coupled networks.
- A theoretical framework for understanding intersimilarity's impact on cascading failures was previously lacking.
Purpose of the Study:
- To develop a theoretical understanding of how intersimilarity affects cascading failures in interdependent networks.
- To map the cascading process in intersimilar systems to a solvable percolation problem.
- To analyze the impact of intersimilarity on cascading failures in Erdős-Rényi (ER) random networks.
Main Methods:
- Mapped the cascading process in intersimilar networks to a percolation problem on subnetworks.
- Analyzed subnetworks composed of common and noncommon links.
- Applied analytical solutions to Erdős-Rényi (ER) network models for common and noncommon links.
Main Results:
- Demonstrated that intersimilarity reduces cascading failures in interdependent networks.
- Showed that for fully coupled ER networks, cascading reduction increases with intersimilarity (K).
- Confirmed that the phase transition in cascading failures remains discontinuous, regardless of intersimilarity level (K≥0).
Conclusions:
- The analytical framework provides a theoretical basis for the observed reduction in cascading failures due to intersimilarity.
- The findings are generalizable to various interdependent random network systems.
- Intersimilarity is a key factor in network resilience against cascading failures, though it does not eliminate abrupt transitions.
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