Abstract
Must Investing more resources to protect every node in a network improve the robustness of the whole network subject to target attacks? To answer this question, we investigate the cascading dynamics in some typical networks. In real networks, the load on a node is generally correlated with the betweenness. Considering the weight of a node, we give a new method to define the initial load on a node by the revised betweenness. Then we present a simple cascading model. We investigate the cascading dynamics by disabling a single key node with the highest load. We find that in BA scale-free networks, the bigger the capacity of every node, the stronger the robustness of the whole network. However, in WS networks and some random networks, when we increase the capacity of every node, instead, the robustness of the whole network is weaker. In US power grid and the China power grid, we also observe this counterintuitive phenomenon. We give a reasonable explanation by a simple illusion. By the analysis, we think that resurrections of some nodes in a ring network structure after removing a node may be the reason of this phenomenon.
Highlights
Must Investing more resources to protect every node in a network improve the robustness of the whole network subject to target attacks? To answer this question, we investigate the cascading dynamics in some typical networks
The betweenness method to assign the initial load on a node or an edge can better reflect the flow of physical quantities in many realistic situations, it may not be practical for very large networks in some real networks such as the Internet or WWW, owing to its consideration of the whole networks topological information
To this end, applying the information of the degree and considering the calculation of the betweenness of a node, we introduce a new method to assign the initial load on this node and construct a cascading model with a tunable parameter
Summary
In WS networks, ring-coupled networks, some ER networks, and Power grid, we surprisingly find a counterintuitive phenomenon, i.e., the improvement of the capacity of every node does not reduce the size of the cascade, instead, the robustness of the network is more weaker. By carefully analyzing the dynamic mechanism of the cascading propagation and the calculating process of the betweenness of a node, we speculate that a kind of the ring structure in the remaining network after removing a node may be a cause of the ability paradox. Starting from a coupled-ring network and according to the rewiring probability on each existing edge, we study the cascading propagation in a serial of networks with the ring structure and observe the ability paradox in our cascading model. Our work may have practical value for controlling various cascading-failure-induced disasters in the real world
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