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Observed social networks are often considered as proxies for underlying social networks. The analysis of observed networks oftentimes involves the identification of influential nodes via various centrality measures. This paper brings insights from research on adversarial attacks on machine learning systems to the domain of social networks by studying strategies by which an adversary can minimally perturb the observed network structure to achieve their target function of modifying the ranking of a target node according to centrality measures. This can represent the attempt of an adversary to boost or demote the degree to which others perceive individual nodes as influential or powerful. We study the impact of adversarial attacks on targets and victims, and identify metric-based security strategies to mitigate such attacks. We conduct a series of controlled experiments on synthetic network data to identify attacks that allow the adversary to achieve their objective with a single move. We then replicate the experiments with empirical network data. We run our experiments on common network topologies and use common centrality measures. We identify a small set of moves that result in the adversary achieving their objective. This set is smaller for decreasing centrality measures than for increasing them. For both synthetic and empirical networks, we observe that larger networks are less prone to adversarial attacks than smaller ones. Adversarial moves have a higher impact on cellular and small-world networks, while random and scale-free networks are harder to perturb. Also, empirical networks are harder to attack than synthetic networks. Using correlation analysis on our experimental results, we identify how combining measures with low correlation can aid in reducing the effectiveness of adversarial moves. Our results also advance the knowledge about the robustness of centrality measures to network perturbations. The notion of changing social network data to yield adversarial outcomes has practical implications, e.g., for information diffusion on social media, influence and power dynamics in social systems, and developing solutions to improving network security. [ABSTRACT FROM AUTHOR]