Percolation in multilayer complex networks with connectivity and interdependency topological structures.

• The percolation in double-layer networks with both connectivity and interdependency links is studied. • The manners of percolation transition can be categorized into first-order, second-order and double phase transitions. • A theory to calculate the percolation transition points and the switching point of percolation types has been derived. • Our results is in concordance with the real observations of cascading failures qualitatively. The concept of a multilayer network describes a typical class of networks that have multiple types of links, that represent the different natures of interactions among nodes. In this work, we investigate the cascading dynamics in double-layer networks with two topological layers composed of connectivity links and interdependency links. The failure of a node can disable the nodes that disconnect the viable nodes, but it can also cause some amount of damage to its interdependency neighbours. We find that the characteristics of the percolation transition can be categorized into three types: first-order, second-order and double phase transition, which depend on the interdependency strength among nodes and the density of interdependency links of the system. We develop a theoretical framework to predict the percolation transition points and the switching point of percolation types. We have also validated our model in a double-layer empirical network composed by an internet and a power grid, and found that the results reproduced by our model is in concordance with the observations of cascading failures occurred in the critical infrastructure systems. Our work not only gives a possible qualitative explanation for the unexpected large-scale damages or disruptive avalanches in real-world infrastructure systems, but it also provides enlightening significance for how the double-layer network can be designed to have a satisfying resilience level. [ABSTRACT FROM AUTHOR]