Nucleation phenomena and extreme vulnerability of spatial k-core systems
Leyang Xue1,2,3, Shengling Gao3,4, Lazaros K Gallos5
1International Academic Center of Complex Systems, Beijing Normal University, Zhuhai, 519087, China.
Nature Communications
|July 11, 2024
Summary
K-core percolation in spatially embedded networks shows connection length controls transition types. A metastable phase allows localized damage to trigger system-wide collapse, similar to nucleation.
Area of Science:
- Complex networks
- Statistical physics
- Network science
Background:
- K-core percolation is a key dynamical process in complex networks.
- Previous studies on random networks revealed mixed-order transitions.
- Real-world networks are spatially embedded, not random.
Purpose of the Study:
- Investigate k-core percolation on 2D spatially embedded networks.
- Determine the influence of connection length on transition types.
- Explore phenomena in different phase transitions.
Main Methods:
- Analysis of k-core percolation dynamics.
- Modeling on two-dimensional spatially embedded network structures.
- Characterization of phase transitions and critical phenomena.
Main Results:
- Connection length dictates transition type, unlike in random networks.
- Discovered four distinct phase transition types and a rich phase diagram.
- Identified a metastable phase where local damage causes macroscopic collapse.
Conclusions:
- Spatial embedding fundamentally alters k-core percolation dynamics.
- Connection length is a critical parameter controlling network stability.
- The metastable phase exhibits nucleation-like behavior, with implications for network resilience.
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