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Optimizing interconnections to maximize the spectral radius of interdependent networks
Huashan Chen1,2,3, Xiuyan Zhao2, Feng Liu1
1State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China.
Physical Review. E
|April 19, 2017
Summary
This study reveals how to maximize the spectral radius of interdependent networks by strategically linking nodes. Optimal interconnections enhance epidemic control and synchronization in complex systems.
Area of Science:
- Network Science
- Complex Systems Analysis
- Mathematical Physics
Background:
- The spectral radius of adjacency matrices is crucial for understanding dynamics in complex networks, influencing processes like synchronization and epidemic spread.
- Existing research primarily focuses on bounding the spectral radius, with less attention paid to its maximization in interdependent network structures.
Purpose of the Study:
- To investigate methods for maximizing the spectral radius of interdependent networks through optimal interconnections.
- To develop and validate algorithms for identifying optimal inter-network links that increase the spectral radius.
Main Methods:
- Derivation of formulas for estimating the spectral radius of interdependent networks.
- Development of algorithms based on eigenvector centrality and network properties for optimal interconnection strategies.
- Extensive simulations to demonstrate the effectiveness of the proposed algorithms across various parameter regimes.
Main Results:
- Formulas for estimating the spectral radius of interdependent networks were derived.
- A suite of algorithms was developed, including a simple method linking high-centrality nodes to specific nodes in the other network.
- Simulations confirmed the applicability and effectiveness of the algorithms in maximizing the spectral radius.
Conclusions:
- Optimal interconnections significantly enhance the spectral radius of interdependent networks.
- The developed algorithms provide practical tools for network design and control.
- Maximizing spectral radius through optimal interconnections can effectively lower epidemic thresholds and improve synchronization in coupled systems.