Critical phenomena in heterogeneous k-core percolation

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.

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• Graph cluster randomization: network exposure to multiple universes
• Cascading failures in interdependent networks with finite functional components
• The fate of the bootstrap percolation hybrid critical point in finite dimension
• Generalized model for $k$-core percolation and interdependent networks
• Insights into bootstrap percolation: Its equivalence with k-core percolation and the giant component
• Failure-recovery model with competition between failures in complex networks: a dynamical approach
• Random node reinforcement and $K$-core structure of complex networks
• Fredrickson-Andersen model on Bethe lattice with random pinning
• The large connectivity limit of bootstrap percolation
• Selective Bootstrap Percolation
• Analytical approach to the dynamics of facilitated spin models on random networks
• Improving the accuracy of the k-shell method by removing redundant links-from a perspective of spreading dynamics