Controllability and observability of cascading failure networks

Cascading failure analysis in previous existing works has mainly focused on random or intentional local attacks, and how to control these failures in complex networks with minimum input from the external signals is a new way of understanding cascades from a global view of network control. In this paper, we are motivated to develop a new framework, which first transforms the original networks (ONs) into cascading failure networks (CFNs) via the attack on each single node. Then, we study the controllability of the CFNs, and try to disclose the cascading failures of the ONs by network control. Furthermore, we analyze the impact of network structure dynamics on the framework. The results show that large-scale cascades are more likely to be triggered by hub node attacks in sparse and inhomogeneous networks, which need more driver nodes in order for them to be controlled. The driver nodes in the CFNs tend to avoid the high-degree nodes in the ONs, and this tendency enhances the homogeneous networks. In addition, networks with strong community strength and heterogeneous community sizes are more robust against attacks, and are easier to control. We also find that the degree distribution of the ONs mainly determines the size of the CFNs, as well as the minimum number of driver nodes, and the latter is also applicable to their observability. Furthermore, a similar impact on the CFNs can be observed by increasing the number of links as well as the capacity of the nodes in the ONs.