Network members can hide from group centrality measures

Group centrality measures assess the relative importance of a set of nodes within a network. In many settings, certain groups may have a strong incentive to evade such analysis—either to avoid detection, obscure their role, or limit exposure. While evasion has been studied in the context of individual centrality, no prior work has investigated how groups might strategically rewire a network to minimize their group centrality. In this work, we address this gap by analyzing the computational aspects of hiding from three fundamental group centrality measures, namely degree, closeness, and betweenness. We show that the problem of finding an optimal rewiring strategy can be solved in polynomial time for degree group centrality, but is NP -complete for closeness and betweenness group centrality measures. Furthermore, we provide a mixed-integer linear program for computing an optimal hiding strategy against closeness group centrality in networks of moderate size. We complement our theoretical findings with an extensive empirical evaluation comparing optimal and heuristic strategies across various network topologies and evader distributions. Our results demonstrate that evasion is often possible even when the evading group has access only to information about its immediate network neighborhood, and that certain heuristics perform consistently well across a range of scenarios. This work provides a foundation for understanding and mitigating the risks posed by groups seeking to conceal their centrality in complex networks.