Singularities in ternary mixtures of k-core percolation

TL;DR

This paper investigates heterogeneous k-core percolation in ternary node mixtures, revealing a new critical phenomenon with implications for network resilience and glass systems.

Contribution

It introduces a novel critical behavior in ternary mixtures of node types within k-core percolation models, expanding understanding of network stability.

Findings

Identification of a new critical phenomenon in ternary mixtures

Analytical framework applicable to various network topologies

Potential applications in infrastructure stability and glass physics

Abstract

Heterogeneous k-core percolation is an extension of a percolation model which has interesting applications to the resilience of networks under random damage. In this model, the notion of node robustness is local, instead of global as in uniform k-core percolation. One of the advantages of k-core percolation models is the validity of an analytical mathematical framework for a large class of network topologies. We study ternary mixtures of node types in random networks and show the presence of a new type of critical phenomenon. This scenario may have useful applications in the stability of large scale infrastructures and the description of glass-forming systems.