Enhancing the robustness of interdependent networks by positively correlating a portion of nodes

Cascading failures caused by interdependencies make modern coupled systems extremely fragile to failures. In existing network robustness enhancing methods, maximizing interlayer degree-degree correlations has been proven to be an effective way to improve the robustness of interdependent networks under random failures. Here, we propose a Portion of Nodes positively Correlated strategy (PNC) to improve network robustness by positively correlating a portion of nodes, in which the nodes that are positively correlated are selected in descending order of degree, starting at a cutoff value. Based on percolation theory, we verify the effectiveness of PNC on different networks. And find that, when the nodes with the highest degree are preferentially correlated, i.e., the cutoff value takes the maximum degree, this strategy achieves a state-of-the-art optimization effect. In particular, for interdependent scale-free networks with power-law exponent $\gamma$ that satisfies $2<\gamma<3$, we theoretically demonstrate that the highest Degree Preferentially Correlated mode (DPC) can maximize network robustness by changing the coupling state of the near $0$ proportion of nodes. For $\gamma=3$, such a mode can make the network turn into a second-order phase transition at the collapse point. Finally, we discuss the relationship between the robustness of optimized networks and common links in real-world interdependent networks.