Cluster aggregation model for discontinuous percolation transition

Abstract

The evolution of the Erdős-Rényi (ER) network by adding edges can be viewed as a cluster aggregation process. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel $K_{ij}\sim ij$, where $ij$ is the product of the sizes of two merging clusters. Here, we study more general cases in which $K_{ij}$ is sub-linear as $K_{ij}\sim (ij{)}^{\omega }$ with $0\le \omega <1/2$; we find that the percolation transition (PT) is discontinuous. Moreover, PT is also discontinuous when the ER dynamics evolves from proper initial conditions. The rate equation approach for such discontinuous PTs enables us to uncover the mechanism underlying the explosive PT under the Achlioptas process.

5 pages, 5 figures

References in corpus (4)

• Explosive percolation in scale-free networks
• Percolation Transitions in Scale-Free Networks under Achlioptas Process
• Construction and Analysis of Random Networks with Explosive Percolation
• Evolution of scale-free random graphs: Potts model formulation

Cited by in corpus (60)

• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• 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 via control of the largest cluster
• Statistical physics approaches to the complex Earth system
• Explosive Percolation: Novel critical and supercritical phenomena
• Recent advances and open challenges in percolation
• Local cluster aggregation models of explosive percolation
• 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
• Tricritical point in explosive percolation
• A new route to Explosive Percolation
• Continuity of the Explosive Percolation Transition
• Hybrid Percolation Transition in Cluster Merging Processes: Continuously Varying Exponents
• 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
• 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
• Solution of the explosive percolation quest. II. Infinite-order transition produced by the initial distributions of clusters
• Transport on exploding percolation clusters
• Critical phenomena in heterogeneous k-core percolation
• Diverse types of percolation transitions
• Discontinuous percolation transitions in real physical systems
• Unstable supercritical discontinuous percolation transitions
• Clusters and the entropy in opinion dynamics on complex networks
• Correlated percolation and tricriticality
• Criterion for explosive percolation transitions on complex networks
• Critical exponents of the explosive percolation transition
• About the fastest growth of Order Parameter in Models of Percolation
• Two Types of Discontinuous Percolation Transitions in Cluster Merging Processes
• Non-Local Product Rules for Percolation
• Controlling percolation with limited resources
• Transmission of packets on a hierarchical network: Statistics and explosive percolation
• Unified framework for hybrid percolation transitions based on microscopic dynamics
• Social Climber attachment in forming networks produces phase transition in a measure of connectivity
• Watersheds and Explosive percolation
• Explosive Ising
• Genuine Non-Self-Averaging and Ultra-Slow Convergence in Gelation
• Exact combinatorial approach to finite coagulating systems
• Discontinuous percolation in diffusion-limited cluster aggregation
• Scaling relations and finite-size scaling in gravitationally correlated lattice percolation models
• Spectral Anlysis on Explosive Percolation
• Degree product rule tempers explosive percolation in the absence of global information
• Exact combinatorial approach to finite coagulating systems through recursive equations
• Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework
• Degree-dependent network growth: From preferential attachment to explosive percolation
• Percolation Transitions in Growing Networks Under Achlioptas Processes: Analytic Solutions
• Link rewiring with local information--induced hybrid percolation transitions
• Crossover behavior of conductivity in a discontinuous percolation model
• Coalescense with arbitrary-parameter kernels and monodisperse initial conditions: A study within combinatorial framework
• Discontinuous percolation via suppression of neighboring clusters in a network
• Random growth lattice filling model of percolation: a crossover from continuous to discontinuous transition
• Percolation critical exponents in cluster kinetics of pulse-coupled oscillators