ArticleNature communications2024
Nucleation phenomena and extreme vulnerability of spatial k-core systems.
Article in Nature communications, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
The trial behind it
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Who cites it
7 citing papers in PubMed.
- The Efficiency of Clusters on Networks and Their Robustness.Entropy (Basel, Switzerland) · 2026Article
- Temporal self-similarity reveals percolation universality classes in complex networks.Nature communications · 2026Article
- A complex network perspective on brain disease.Biological reviews of the Cambridge Philosophical Society · 2026Review
- Early warning of regime switching in a complex financial system from a spillover network dynamic perspective.iScience · 2025Article
- Hybrid universality classes of systemic cascades.Nature communications · 2025Article
- Physical Realizations of Interdependent Networks: Analogy to Percolation.Entropy (Basel, Switzerland) · 2025Article
- Nucleation phenomena and extreme vulnerability of spatial k-core systems.Nature communications · 2024Article
Corrections and comments
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Authors and funding
7 authors.
Funding
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.
Identifiers
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.