Recent advancements in graph unlearning models have enhanced model utility by preserving the node representation essentially invariant, while using gradient ascent on the forget set to achieve unlearning. However, this approach causes a drastic degradation in model utility during the unlearning process due to the rapid divergence speed of gradient ascent. In this paper, we introduce \textbf{INPO}, an \textbf{I}nfluence-aware \textbf{N}egative \textbf{P}reference \textbf{O}ptimization framework that focuses on slowing the divergence speed and improving the robustness of the model utility to the unlearning process. Specifically, we first analyze that NPO has slower divergence speed and theoretically propose that unlearning high-influence edges can reduce impact of unlearning. We design an influence-aware message function to amplify the influence of unlearned edges and mitigate the tight topological coupling between the forget set and the retain set. The influence of each edge is quickly estimated by a removal-based method. Additionally, we propose a topological entropy loss from the perspective of topology to avoid excessive information loss in the local structure during unlearning. Extensive experiments conducted on five real-world datasets demonstrate that INPO-based model achieves state-of-the-art performance on all forget quality metrics while maintaining the model's utility. Codes are available at \href{https://github.com/sh-qiangchen/INPO}{https://github.com/sh-qiangchen/INPO}.

As concerns over data privacy intensify, unlearning in Graph Neural Networks (GNNs) has emerged as a prominent research frontier in academia. This concept is pivotal in enforcing the \textit{right to be forgotten}, which entails the selective removal of specific data from trained GNNs upon user request. Our research focuses on edge unlearning, a process of particular relevance to real-world applications. Current state-of-the-art approaches like GNNDelete can eliminate the influence of specific edges yet suffer from \textit{over-forgetting}, which means the unlearning process inadvertently removes excessive information beyond needed, leading to a significant performance decline for remaining edges. Our analysis identifies the loss functions of GNNDelete as the primary source of over-forgetting and also suggests that loss functions may be redundant for effective edge unlearning. Building on these insights, we simplify GNNDelete to develop \textbf{Unlink to Unlearn} (UtU), a novel method that facilitates unlearning exclusively through unlinking the forget edges from graph structure. Our extensive experiments demonstrate that UtU delivers privacy protection on par with that of a retrained model while preserving high accuracy in downstream tasks, by upholding over 97.3\% of the retrained model's privacy protection capabilities and 99.8\% of its link prediction accuracy. Meanwhile, UtU requires only constant computational demands, underscoring its advantage as a highly lightweight and practical edge unlearning solution.