Based on the MMA concept, we have proposed a model of interdependent MMA networks, where any node with degree k can be an MMA node with probability kγ. Here, if an MMA node disconnects from the giant component, it can use other methods to reestablish a connection. We have theoretically analyzed the percolation process of the proposed model and derived equations for the giant component. Furthermore, we introduced a method to calculate the discontinuous phase transition point for interdependent networks with arbitrary degree distributions. In addition, our simulation results agree well with our theoretical analyses. We found that the discontinuous phase transition point decreases with increasing γ, and, when γ is greater than a certain value, the phase transition type transfers to continuous. In conclusion, interdependent networks become more robust with an increasing number of MMA nodes.

基于MMA概念，我们提出了一个相互依赖的MMA网络模型，其中任何度数为k的节点都可以是概率为kγ的MMA节点。在这里，如果MMA节点与巨型组件断开连接，则它可以使用其他方法重新建立连接。我们从理论上分析了所提出模型的渗流过程和巨型组件的导出方程。此外，我们介绍了一种计算具有任意度分布的相互依赖网络的不连续相变点的方法。此外，我们的仿真结果与我们的理论分析非常吻合。我们发现，不连续相变点随γ的增加而降低，而当γ时，大于某个值时，相变类型转换为连续。总之，随着MMA节点数量的增加，相互依赖的网络变得更加健壮。