-selective percolation: A simple model leading to a rich repertoire of phase transitions
arXiv:2109.15069 · doi:10.1063/5.0081253
Abstract
We propose the -selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree is deactivated one by one until no more nodes with degree remain. The non-monotonic response of the giant component size on various synthetic and real-world networks implies a conclusion that a network can be more robust against such selective attack by removing further edges. In the theoretical perspective, the -selective percolation process exhibits a rich repertoire of phase transitions, including double transitions of hybrid and continuous, as well as reentrant transitions. Notably, we observe a tricritical-like point on Erdős-Rényi networks. We also examine a discontinuous transition with unusual order parameter fluctuation and distribution on simple cubic lattices, which does not appear in other percolation models with cascade processes. Finally, we perform finite-size scaling analysis to obtain critical exponents on various transition points, including those exotic ones.
arXiv comment10 pages, 8 figures
References in corpus (22)
- Error and attack tolerance of complex networks
- Random graphs with arbitrary degree distributions and their applications
- Network robustness and fragility: Percolation on random graphs
- Attack vulnerability of complex networks
- Breakdown of the Internet under intentional attack
- Cascade control and defense in complex networks
- k-core organization of complex networks
- Percolation on complex networks: Theory and application
- Explosive Phenomena in Complex Networks
- Bond and Site Percolation in Three Dimensions
- Explosive Percolation: Novel critical and supercritical phenomena
- Recent advances and open challenges in percolation
- Finite-size scaling in complex networks
- Avoiding a Spanning Cluster in Percolation Models
- Are Percolation Transitions always Sharpened by Making Networks Interdependent?
- Recent advances of percolation theory in complex networks
- Hybrid Phase Transition into an Absorbing State: Percolation and Avalanches
- Random graph approach to multifunctional molecular networks
- Critical behavior of -core percolation: Numerical studies
- Percolation transitions in the survival of interdependent agents on multiplex networks, catastrophic cascades, and SOS
- Critical behaviors of high-degree adaptive and collective-influence percolation
- Selective Bootstrap Percolation