Cascade defense via navigation in scale free networks

In this paper, we investigate cascade defense and control in scale free networks via navigation strategy. It is found that with an appropriate parameter a, which is tunable in controlling the effect of degree in the navigation strategy, one can reduce the risk of cascade break down. By checking the distribution of efficient betweenness centrality (EBC) and the average EBC of vertices with degree k, the validity can be guaranteed. Despite the advantage of cascade defense, the degree based navigation strategy may also lead to lower network efficiency. To avoid this disadvantage, we propose a new navigation strategy. Importantly and interestingly, the new strategy can defend cascade break down effectively even without reducing the network efficiency. Distribution of the EBC and EBC-degree correlation of the new strategy are also investigated to explain the effectiveness in cascade defense.