Tricritical point in heterogeneous k-core percolation

TL;DR

This paper investigates a binary mixture of heterogeneous k-core percolation, revealing a tricritical point and analyzing its critical behavior through analytical and computational methods on different network types.

Contribution

It identifies a tricritical point in heterogeneous k-core percolation and characterizes its critical exponents using new analytical and computational approaches.

Findings

Discovery of a tricritical point in heterogeneous k-core percolation.

Calculation of critical exponents for different network structures.

Identification of a new scaling scenario in percolation transitions.

Abstract

k-core percolation is an extension of the concept of classical percolation and is particularly relevant to understand the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous k-cores, where each vertex is assigned a local threshold k_i. In this paper we identify a binary mixture of heterogeneous k-core which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erdos-Renyi networks and 2d square lattices.