Classical Percolation, Generalized Percolation and Cascades

Abstract

AbstractThis chapter characterizes the robustness of multiplex and multilayer networks using classical percolation, directed percolation and antagonistic percolation. Classical percolation determines whether a finite fraction of nodes of the multilayer networks are connected by any type of connection. Classical percolation can be affected by multiplexity since the degree correlations among different layers can modulate the robustness of the entire multilayer network. Directed percolation describes the propagation of a disease requiring cooperative infection from different layers of the multiplex network. It displays a rich phase diagram including both continuous and discontinuous phase transitions. Antagonist percolation on a duplex network describes the competition between two layers and can give rise to hysteresis loops corresponding to phases that either one layer or the other can percolate Avalanches generated by the generalized Sandpile Model and Watts–Strogatz Model are also discussed, emphasizing their relevance for studying the stability of power grids and financial systems.