Dynamics of k-core percolation

TL;DR

This paper investigates the behavior of k-core percolation in various network types, revealing different avalanche dynamics associated with first and second order phase transitions.

Contribution

It provides a comparative analysis of avalanche behaviors in k-core percolation across different network structures and transition orders.

Findings

Power-law avalanches in first order k-core systems

Truncated avalanches in second order k-core systems

Simulation results across multiple network types

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.