Dynamics of k-core percolation in a random graph

Abstract

We study the edge deletion process of random graphs near a k-core percolation point. We find that the time-dependent number of edges in the process exhibits critically divergent fluctuations. We first show theoretically that the k-core percolation point is exactly given as the saddle-node bifurcation point in a dynamical system. We then determine all the exponents for the divergence based on a universal description of fluctuations near the saddle-node bifurcation.

16 pages, 4 figures

References in corpus (15)

• k-core organization of complex networks
• Vibrations and diverging length scales near the unjamming transition
• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Diverging length scale and upper critical dimension in the Mode-Coupling Theory of the glass transition
• Jamming Percolation and Glass Transitions in Lattice Models
• Facilitated spin models on Bethe lattice: bootstrap percolation, mode-coupling transition and glassy dynamics
• Finite size scaling for the core of large random hypergraphs
• Hysteresis in the Random Field Ising Model and Bootstrap Percolation
• First-order rigidity transition on Bethe Lattices
• $1/d$ Expansion for $k$-Core Percolation
• On $k$-Core Percolation in Four Dimensions
• Critical phenomena in globally coupled excitable elements
• Dynamics of k-core percolation
• A theory for critically divergent fluctuations of dynamical events at non-ergodic transitions

Cited by in corpus (12)

• Percolation on complex networks: Theory and application
• Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
• Critical dynamics of the k-core pruning process
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Bootstrap percolation and kinetically constrained models on hyperbolic lattices
• A universal form of slow dynamics in zero-temperature random-field Ising model
• Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation
• Thermodynamics of the Fredrickson-Andersen Model on the Bethe Lattice
• Multi-step relaxations in Glauber dynamics of a bond-diluted Ising model on a Bethe lattice
• Morphology transition at depinning in a solvable model of interface growth in a random medium
• Singular perturbation near mode-coupling transition
• Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model