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Temporal self-similarity reveals percolation universality classes in complex networks
Sheng Fang1, Jun Meng2, Qing Lin1
1School of Systems Science, Beijing Normal University, Beijing, China.
Nature Communications
|July 13, 2026
Summary
Complex systems exhibit temporal self-similarity in fragmentation dynamics. Two critical exponents characterize universality classes, revealing distinct real-world network behaviors from idealized models.
Area of Science:
- Complex systems science
- Statistical physics
- Network science
Background:
- Catastrophic fragmentation and structural transitions are common in complex systems.
- Universality classes governing these dynamics are often unclear due to heterogeneity and lack of clear thresholds.
Purpose of the Study:
- To discover a universal phenomenon governing dynamic percolation across complex networks.
- To establish a framework for characterizing universality classes and critical exponents in heterogeneous systems.
Main Methods:
- Tracking statistics of incremental growth events in dynamic percolation.
- Identifying and analyzing Fisher-type critical exponents (τc and τs).
- Developing scaling relations to derive other critical exponents.
Main Results:
- Discovered temporal self-similarity in dynamic percolation across diverse networks.
- Fragmentation dynamics are governed by two independent critical exponents, τc and τs.
- Real-world networks (biological, social, infrastructural) show distinct universality classes compared to idealized models.
Conclusions:
- Established a dynamic paradigm bridging statistical physics and real-world resilience.
- Developed a parameter-free, scalable approach to classify structural vulnerabilities in heterogeneous systems.
- Highlighted the impact of higher-order structural features on network dynamics.
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