Explosive percolation via control of the largest cluster

Abstract

We show that only considering the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the transition point, yielding a fractal dimension of $1.23\pm 0.03$, close to that of watersheds.

4 pages, 5 figures, final version

References in corpus (9)

• Universality classes in nonequilibrium lattice systems
• Explosive percolation in scale-free networks
• Percolation Transitions in Scale-Free Networks under Achlioptas Process
• Construction and Analysis of Random Networks with Explosive Percolation
• Explosive percolation: a numerical analysis
• Local cluster aggregation models of explosive percolation
• Cluster aggregation model for discontinuous percolation transition
• A Hamiltonian approach for explosive percolation
• New efficient methods to calculate watersheds

Cited by in corpus (103)

• Catastrophic cascade of failures in interdependent networks
• Recent advances in percolation theory and its applications
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• "Explosive Percolation" Transition is Actually Continuous
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Explosive Phenomena in Complex Networks
• Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
• Explosive Percolation: Novel critical and supercritical phenomena
• Recent advances and open challenges in percolation
• Avoiding a Spanning Cluster in Percolation Models
• Suppressing epidemic spreading in multiplex networks with social-support
• Strongly discontinuous explosive percolation with multiple giant components
• Scaling behavior of explosive percolation on the square lattice
• Ordinary Percolation with Discontinuous Transitions
• Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
• Are Percolation Transitions always Sharpened by Making Networks Interdependent?
• Critical behaviors in contagion dynamics
• Tricritical point in explosive percolation
• Recent advances of percolation theory in complex networks
• Continuity of the Explosive Percolation Transition
• Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents
• Rare events and discontinuous percolation transitions
• Fracturing highly disordered materials
• Explosive oscillation death in coupled Stuart-Landau oscillators
• Impact of embedding on predictability of failure-recovery dynamics in networks
• Phase transitions in the q-voter model with noise on a duplex clique
• Epidemic reemergence in adaptive complex networks
• Solution of the explosive percolation quest: Scaling functions and critical exponents
• Anomalous discontinuity at the percolation critical point of active gels
• Finite-size scaling theory for explosive percolation transitions
• Using explosive percolation in analysis of real-world networks
• Crackling Noise in Fractional Percolation -- Randomly distributed discontinuous jumps in explosive percolation
• Fracturing ranked surfaces
• Explosive site percolation and finite size hysteresis
• Gaussian model of explosive percolation in three and higher dimensions
• Suppression effect on explosive percolations
• Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
• Connectivity disruption sparks explosive epidemic spreading
• Optimal path cracks in correlated and uncorrelated lattices
• Deriving an underlying mechanism for discontinuous percolation
• Explosive site percolation with a product rule
• Transport on exploding percolation clusters
• Diverse types of percolation transitions
• Critical phenomena in heterogeneous k-core percolation
• Impact of Perturbations on Watersheds
• Discontinuous percolation transitions in real physical systems
• Explosive Percolation: Unusual Transitions of a Simple Model
• Scaling Relations for Watersheds
• Unstable supercritical discontinuous percolation transitions
• Fundamental ingredients for the emergence of discontinuous phase transitions in the majority vote model
• Crossover phenomena of percolation transition in evolution networks with hybrid attachment
• Criterion for explosive percolation transitions on complex networks
• Changes in the gradient percolation transition caused by an Allee effect
• About the fastest growth of Order Parameter in Models of Percolation
• Critical exponents of the explosive percolation transition
• Corrections to Scaling for Watersheds, Optimal Path Cracks, and Bridge Lines
• Two Types of Discontinuous Percolation Transitions in Cluster Merging Processes
• Weakly Explosive Percolation in Directed Networks
• Scaling of Clusters near Discontinuous Percolation Transitions in Hyperbolic Networks
• Stacked triangular lattice: Percolation properties
• No-enclave percolation corresponds to holes in the cluster backbone
• Non-Local Product Rules for Percolation
• A percolation model with continuously varying exponents
• Explosive percolation in graphs
• Controlling percolation with limited resources
• How to share underground reservoirs
• Transmission of packets on a hierarchical network: Statistics and explosive percolation
• Percolation model with an additional source of disorder
• Social Climber attachment in forming networks produces phase transition in a measure of connectivity
• Critical phenomena of a hybrid phase transition in cluster merging dynamics
• Watersheds and Explosive percolation
• Explosive Ising
• Explosive percolation in finite dimensions
• Information entropy of classical versus explosive percolation
• Criticality and Continuity of Explosive Site Percolation in Random Networks
• A minimal exactly solved model with the extreme Thouless effect
• Alternative criterion for two-dimensional wrapping percolation
• Product-Sum universality and Rushbrooke inequality in explosive percolation
• Genuine Non-Self-Averaging and Ultra-Slow Convergence in Gelation
• Exact evaluation of the cutting path length in a percolation model on a hierarchical network
• Analysis on the evolution process of BFW-like model with explosive percolation of multiple giant components
• Explosive dismantling of two-dimensional random lattices under betweenness centrality attacks
• Scaling relations and finite-size scaling in gravitationally correlated lattice percolation models
• How the site degree influences quantum probability on inhomogeneous substrates
• Mixed-order phase transition in a minimal, diffusion based spin model
• Spectral Anlysis on Explosive Percolation
• Scaling behavior of information entropy in explosive percolation transitions
• Link rewiring with local information--induced hybrid percolation transitions
• Explosive rigidity percolation in kirigami
• Universality class of explosive percolation in Barabási-Albert networks
• Crossover behavior of conductivity in a discontinuous percolation model
• Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition
• Jamming as a random first-order percolation transition
• Discontinuous percolation via suppression of neighboring clusters in a network
• Network-Growth Rule Dependence of Fractal Dimension of Percolation Cluster on Square Lattice
• A Novel Approach to Discontinuous Bond Percolation Transition
• Universality in boundary domain growth by sudden bridging
• Discontinuous transition in explosive percolation via local suppression
• Anomalous percolation transitions beyond the BKT transition in growing networks
• Evolution of autocatalytic sets in a competitive percolation model
• Discontinuous emergence of a giant cluster in assortative scale-free networks
• Explosive rigidity percolation in origami