Criterion for explosive percolation transitions on complex networks
arXiv:1102.0734 · doi:10.1103/PhysRevE.83.032101
Abstract
In a recent Letter, Friedman and Landsberg discussed the underlying mechanism of explosive phase transitions on complex networks [Phys. Rev. Lett. 103, 255701 (2009)]. This Brief Report presents a modest, though more insightful extension of their arguments. We discuss the implications of their results on the cluster-size distribution and deduce that, under general conditions, the percolation transition will be explosive if the mean number of nodes per cluster diverges in the thermodynamic limit and prior to the transition threshold. In other words, if, upon increase of the network size n the amount of clusters in the network does not grow proportionally to n, the percolation transition is explosive. Simulations and analytical calculations on various models support our findings.
References in corpus (16)
- Resilience of the Internet to random breakdowns
- Critical phenomena in complex networks
- "Explosive Percolation" Transition is Actually Continuous
- Second look at the spread of epidemics on networks
- Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
- Self-organized adaptation of a simple neural circuit enables complex robot behaviour
- Explosive percolation in scale-free networks
- Explosive percolation via control of the largest cluster
- Construction and Analysis of Random Networks with Explosive Percolation
- How to make a fragile network robust and vice versa
- Explosive percolation: a numerical analysis
- Local cluster aggregation models of explosive percolation
- Cluster aggregation model for discontinuous percolation transition
- A new route to Explosive Percolation
- A Hamiltonian approach for explosive percolation
- Biased Percolation on Scale-free Networks
Cited by in corpus (18)
- Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
- Explosive Phenomena in Complex Networks
- Explosive Percolation is Continuous, but with Unusual Finite Size Behavior
- Explosive Percolation: Novel critical and supercritical phenomena
- Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
- Recent advances of percolation theory in complex networks
- Anomalous discontinuity at the percolation critical point of active gels
- Gaussian model of explosive percolation in three and higher dimensions
- Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition
- Achlioptas processes are not always self-averaging
- Two Types of Discontinuous Percolation Transitions in Cluster Merging Processes
- Non-Local Product Rules for Percolation
- Watersheds and Explosive percolation
- Degree product rule tempers explosive percolation in the absence of global information
- Emergence of biconnected clusters in explosive percolation
- Degree-dependent network growth: From preferential attachment to explosive percolation
- Explosive percolation on the Bethe lattice is ordinary
- Kinetics of Aggregation with Choice