The problem of hiding a node inside of a network in the presence of an unauthorized crawler has been shown to be NP-complete. The available heuristics tackle this problem from mainly two perspectives: (1) the local immediate neighborhood of the target node (local perturbation models) and (2) the global structure of the graph (global perturbation models). While the objective of both is similar (i.e., decreasing the centrality of the target node), they vary substantially in their performance and efficiency; the global measures are computationally inefficient in the real-world scenarios, while the local perturbation methods deal with the problem of constrained performance. In this study, we propose a community-based heuristic, CoVerD, that retains both the computational efficiency of local methods and the superior performance of global methods in minimizing the target’s closeness centrality. Our experiments on five real-world networks show a significant increase in performance by using CoVerD against both BFS and DFS crawling attacks. In some instances, our algorithm successfully increased the crawler’s budget by 3 and 10 times compared to the next best-performing benchmark. The results of this study show the importance of the local community structure in preserving the privacy of the nodes in a network, and pave a promising path for designing scalable and effective network protection models.