Nucleation phenomena and extreme vulnerability of spatial k-core systems

Leyang Xue, Shengling Gao, Lazaros K. Gallos (), Orr Levy, Bnaya Gross, Zengru Di () and Shlomo Havlin ()
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Leyang Xue: Beijing Normal University
Shengling Gao: Bar-Ilan University
Lazaros K. Gallos: Rutgers University
Orr Levy: Yale University School of Medicine
Bnaya Gross: Bar-Ilan University
Zengru Di: Beijing Normal University
Shlomo Havlin: Bar-Ilan University

Nature Communications, 2024, vol. 15, issue 1, 1-10

Abstract: Abstract K-core percolation is a fundamental dynamical process in complex networks with applications that span numerous real-world systems. Earlier studies focus primarily on random networks without spatial constraints and reveal intriguing mixed-order transitions. However, real-world systems, ranging from transportation and communication networks to complex brain networks, are not random but are spatially embedded. Here, we study k-core percolation on two-dimensional spatially embedded networks and show that, in contrast to regular percolation, the length of connections can control the transition type, leading to four different types of phase transitions associated with interesting phenomena and a rich phase diagram. A key finding is the existence of a metastable phase where microscopic localized damage, independent of system size, can cause a macroscopic phase transition, a result which cannot be achieved in traditional percolation. In this case, local failures spontaneously propagate the damage radially until the system collapses, a phenomenon analogous to the nucleation process.

Date: 2024
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DOI: 10.1038/s41467-024-50273-5

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