Core percolation on complex networks

Double percolation phase transition in clustered complex networks

We perform an extensive numerical study of the effects of clustering on the structural properties of complex networks. We observe that strong clustering in heterogeneous networks induces the emergence of a core-periphery organization that has a critical effect on their percolation properties. In such situation, we observe a novel double phase transition, with an intermediate phase where only th...

Connecting Core Percolation and Controllability of Complex Networks

Core percolation is a fundamental structural transition in complex networks related to a wide range of important problems. Recent advances have provided us an analytical framework of core percolation in uncorrelated random networks with arbitrary degree distributions. Here we apply the tools in analysis of network controllability. We confirm analytically that the emergence of the bifurcation in...

$k$-core percolation on complex networks: Comparing random, localized and targeted attacks

The type of malicious attack inflicting on networks greatly influences their stability under ordinary percolation in which a node fails when it becomes disconnected from the giant component. Here we study its generalization, k-core percolation, in which a node fails when it loses connection to a threshold k number of neighbors. We study and compare analytically and by numerical simulations of k...

Core percolation on complex networks: Supplemental Material

Inducing effect on the percolation transition in complex networks.

Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always ca...