Inhomogeneous percolation on multilayer networks

Abstract

A generalization of high-order inhomogeneous bond percolation is studied on a multilayer finite fixed network (MFFN) and a multilayer infinite random network (MIRN). The inhomogeneous bond percolation means that edges in different layers are occupied or removed with distinct probabilities, independently and randomly. Firstly, an analytical approach to simplify the inhomogeneous bond percolation on MFFN is presented, by decomposing the layers into disjoint ones, fusing inhomogeneous bond percolation process and combining weighted layers together to form a monolayer network. Then employing generalised recursive approach, discrete-time dynamical system analysis and fixed-point iteration method, we derive the results for percolating probability and the critical occupation probability, demonstrate the percolation transition and critical phenomenon of inhomogeneous bond percolation on these two networks. It is found that, for inhomogeneous bond percolation on MFFN, the high fraction of intersection speeds up the percolating process; for inhomogeneous bond percolation on MIRN, the increasing mean degree will enlarge the supercritical region and enhance the intensity of percolating process.