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Due to the harsh surroundings and violent nature of wireless sensor network (WSN) applications, the network sometimes suffers a large-scale damage that involves several nodes and would thus create multiple disjoint partitions. This paper investigates a strategy for recovering from such damage through the placement of relay nodes (RNs) and promotes a novel approach. The proposed approach opts to reestablish connectivity (i.e., 1-vertex connectivity) using the least number of relays while ensuring a certain quality in the formed topology. Unlike contemporary schemes that often form a minimum spanning tree among the isolated segments, the proposed approach establishes a topology that resembles a spider web, for which the segments are situated at the perimeter. Such a topology not only exhibits stronger connectivity than a minimum spanning tree but achieves better sensor coverage and enables balanced distribution of traffic load among the employed relays as well. To further increase the robustness of the formed topology, the SpiderWeb approach is further extended so that the final topology is guaranteed to be 2-vertex connected. Both centralized and distributed implementations of the SpiderWeb approach are discussed. The simulation results demonstrate the effectiveness of the proposed recovery algorithm.