Abstract: Graphon models provide a flexible nonparametric framework for estimating latentconnectivity probabilities in networks, enabling a range of downstream applicationssuch as link prediction and data augmentation. However, accurate graphon estima-tion typically requires a large graph, whereas in practice, one often only observes asmall-sized network. One approach to addressing this issue is to adopt a transferlearning framework, which aims to improve estimation in a small target graph byleveraging structural information from a larger, related source graph. In this paper,we propose a novel method, namely GTRANS, a transfer learning framework thatintegrates neighborhood smoothing and Gromov-Wasserstein optimal transport toalign and transfer structural patterns between graphs. To prevent negative transfer,GTRANS includes an adaptive debiasing mechanism that identifies and corrects fortarget-specific deviations via residual smoothing. We provide theoretical guaranteeson the stability of the estimated alignment matrix and demonstrate the effectivenessof GTRANS in improving the accuracy of target graph estimation through extensivesynthetic and real data experiments. These improvements translate directly toenhanced performance in downstream applications, such as the graph classificationtask and the link prediction task.