Dynamics of k-core percolation

Abstract

In many network applications nodes are stable provided they have at least k neighbors, and a network of k-stable nodes is called a k-core. The vulnerability to random attack is characterized by the size of culling avalanches which occur after a randomly chosen k-core node is removed. Simulations of lattices in two, three and four dimensions, as well as small world networks, indicate that power-law avalanches occur in first order k-core systems, while truncated avalanches are characteristic of second order cases.

4 pages, 3 figures

References in corpus (17)

• Error and attack tolerance of complex networks
• Crackling Noise
• k-core organization of complex networks
• Statistical Models of Fracture
• Scaling exponents for Barkhausen avalanches in polycrystals and amorphous ferromagnets
• How self-organized criticality works: A unified mean-field picture
• Burst avalanches in solvable models of fibrous materials
• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Fracture model with variable range of interaction
• Crack roughness and avalanche precursors in the random fuse model
• Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices
• Hysteresis in the Random Field Ising Model and Bootstrap Percolation
• First-order rigidity transition on Bethe Lattices
• Clarification of the Bootstrap Percolation Paradox
• $1/d$ Expansion for $k$-Core Percolation
• Universality class for bootstrap percolation with $m=3$ on the cubic lattice
• Threshold value of three dimensional bootstrap percolation

Cited by in corpus (11)

• Percolation on complex networks: Theory and application
• Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
• Large deviations of cascade processes on graphs
• Hysteresis in Random-field Ising model on a Bethe lattice with a mixed coordination number
• Nonequilibrium random-field Ising model on a diluted triangular lattice
• Critical phenomena in globally coupled excitable elements
• Dynamics of k-core percolation in a random graph
• Effect of Coordination Number on Nonequilibrium Critical Point
• Reduction of Dilute Ising Spin Glasses
• Vulnerability and Resilience of Social Engagement: Equilibrium Theory
• Systematic perturbation approach for a dynamical scaling law in a kinetically constrained spin model