Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to mobility, node or edge failures, and varying traffic loads. Percolation theory quantifies the threshold value of a local control parameter such as a node occupation (resp., deletion) probability or an edge activation (resp., removal) probability above (resp., below) which there exists a giant connected component (GCC), a connected component comprising of a number of occupied nodes and active edges whose size is proportional to the size of the network itself. Any pair of occupied nodes in the GCC is connected via at least one path comprised of active edges and occupied nodes. The mere existence of the GCC itself does not guarantee that the long-range connectivity would be robust, e.g. to random link or node failures due to network dynamics. In this paper, we explore new percolation thresholds that guarantee not only spanning network connectivity, but also robustness. We define and analyze four measures of robust network connectivity, explore their interrelationships, and numerically evaluate the respective robust percolation thresholds for the 2D square lattice.

通信网络，电网和运输网络都是网络的示例，即使在由于移动性，节点或边缘故障以及变化的通信量负载而存在通常的网络动态的情况下，其性能也取决于其基础网络组件的可靠连接性。渗流理论对局部控制参数的阈值进行量化，例如在存在巨大连接组件（GCC）的情况下（高于，低于，低于）节点占有（重设，删除）概率或边缘激活（重设，移除）概率。 ），一个连接的组件，由多个占用的节点和有效边组成，其大小与网络本身的大小成比例。GCC中的任一对占用节点都通过至少一条由活动边和占用节点组成的路径连接。健壮的，例如针对由于网络动态而导致的随机链接或节点故障。在本文中，我们探索了新的渗透阈值，这些阈值不仅可以确保跨越网络连接性，而且还可以确保鲁棒性。我们定义并分析了鲁棒网络连通性的四种度量，探索了它们之间的相互关系，并在数值上评估了2D方格的相应鲁棒渗透阈值。