Identification of key recovering node for spatial networks

Many networks in the real world have spatial attributes, such as location of nodes and length of edges, called spatial networks. When these networks are subject to some random or deliberate attacks, some nodes in the network fail, which causes a decline in the network performance. In order to make the network run normally, some of the failed nodes must be recovered. In the case of limited recovery resources, an effective key node identification method can find the key recovering node in the failed nodes, by which the network performance can be recovered most of the failed nodes. We propose two key recovering node identification methods for spatial networks, which are the Euclidean-distance recovery method and the route-length recovery method. Simulations on homogeneous and heterogeneous spatial networks show that the proposed methods can significantly recover the network performance.