Knowledge graphs such as Wikidata serve as valuable resources for structuring and analyzing information across various domains. However, their crowdsourced nature makes them vulnerable to perturbations, including both intentional vandalism and unintentional errors, which can significantly impact rankings derived from these graphs. While previous studies have primarily focused on detecting and preventing entity-level perturbations, this paper investigates the potential impact of such perturbations on the stability of rankings at the structural level, specifically targeting relationships. We formalize the problem of ranking stability under perturbations, and we propose a probabilistic model to assess the likelihood of modifications to knowledge graph relationships changing the ranks of entities. We leverage complex network analysis, in order to evaluate ranking vulnerabilities. Our experimental study demonstrates varying levels of resilience in rankings depending on entity degree distributions and the nature of perturbations.