Critical phenomena in heterogeneous k-core percolation

TL;DR

This paper investigates heterogeneous k-core percolation, revealing critical phenomena such as critical and tricritical points, and classifies the universality classes related to glass transition models.

Contribution

It analytically explores binary mixtures in heterogeneous k-core percolation, identifying conditions for critical phenomena and tricritical points in complex networks.

Findings

Presence of critical and tricritical points in heterogeneous k-core percolation.

A general criterion for the occurrence of tricritical points.

Model's critical exponents match those of facilitated spin models in glass transition studies.

Abstract

$k$-core percolation is a percolation model which gives a notion of network functionality and has many applications in network science. In analysing the resilience of a network under random damage, an extension of this model is introduced, allowing different vertices to have their own degree of resilience. This extension is named heterogeneous $k$-core percolation and it is characterized by several interesting critical phenomena. Here we analytically investigate binary mixtures in a wide class of configuration model networks and categorize the different critical phenomena which may occur. We observe the presence of critical and tricritical points and give a general criterion for the occurrence of a tricritical point. The calculated critical exponents show cases in which the model belongs to the same universality class of facilitated spin models studied in the context of the glass transition.