ArticleProceedings of the National Academy of Sciences of the United States of America2021
Optimal resilience of modular interacting networks.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
- Temporal self-similarity reveals percolation universality classes in complex networks.Nature communications · 2026Article
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- Modeling and analysis of the coupling effect for large-scale multi-band optical networks.Scientific reports · 2025Article
- On the limits of the intervention on complex systems guided by functional networks.Scientific reports · 2025Article
- Unveiling the importance of nonshortest paths in quantum networks.Science advances · 2025Article
- Study on the robust control of higher-order networks.Scientific reports · 2025Article
- Structural robustness of networks with degree-degree correlations between second-nearest neighbors.PloS one · 2025Article
- Cascades Towards Noise-Induced Transitions on Networks Revealed Using Information Flows.Entropy (Basel, Switzerland) · 2024Article
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- Innate but Not Adaptive Immunity Regulates Lung Recovery from Chronic Exposure to Graphene Oxide Nanosheets.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2022Article
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Authors and funding
10 authors.
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Abstract
Coupling between networks is widely prevalent in real systems and has dramatic effects on their resilience and functional properties. However, current theoretical models tend to assume homogeneous coupling where all the various subcomponents interact with one another, whereas real-world systems tend to have various different coupling patterns. We develop two frameworks to explore the resilience of such modular networks, including specific deterministic coupling patterns and coupling patterns where specific subnetworks are connected randomly. We find both analytically and numerically that the location of the percolation phase transition varies nonmonotonically with the fraction of interconnected nodes when the total number of interconnecting links remains fixed. Furthermore, there exists an optimal fraction [Formula: see text] of interconnected nodes where the system becomes optimally resilient and is able to withstand more damage. Our results suggest that, although the exact location of the optimal [Formula: see text] varies based on the coupling patterns, for all coupling patterns, there exists such an optimal point. Our findings provide a deeper understanding of network resilience and show how networks can be optimized based on their specific coupling patterns.
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