Abnormal Behavior in Cascading Dynamics with Node Weight

Considering a preferential selection mechanism of load destination, we introduce a new method to quantify initial load distribution and subsequently construct a simple cascading model. By attacking the node with the highest load, we investigate the cascading dynamics in some synthetic networks. Surprisingly, we observe that for several networks of different structural patterns, a counterintuitive phenomenon emerges if the highest load attack is applied to the system, i.e., investing more resources to protect every node in a network inversely makes the whole network more vulnerable. We explain this ability paradox by analyzing the micro-structural components of the underlying network and therefore reveals how specific structural patterns may influence the cascading dynamics. We discover that the robustness of the network oscillates as the capacity of each node increases. The conclusion of the paper may shed lights on future investigations to avoid the demonstrated ability paradox and subsequent cascading failures in real-world networks.