Tensor-based Spectral Analysis of Cascading Failures over Multilayer Complex Systems

Cascading failure in multilayer complex systems draws significant attentions from both industry and academia nowadays. In this paper, we propose a scalable tensor-based framework to represent the interdependent multilayer network, and use this framework to analyze the failure propagation based on a susceptible-infectious-susceptible (SIS) epidemic model. Specifically, the transition equations and transition tensor are derived to characterize the behavior of failure propagation. We show that the spectral radius of transition tensor is a failure indicator with an explicit failure threshold to measure the system reliability. Moreover, to make the failure indicator analytically tractable and computationally efficient, we derive its upper and lower bounds, as well as its approximated expressions in special cases as functions of the adjacency tensor and epidemic parameters. Our analytical results are evaluated by simulations in a set of multilayer networks generated by random graphs, which show that our results can achieve the desired performance compared with other benchmark approximation methods.