The task of network alignment aims to identify corresponding nodes across multiple networks, with applications in various fields such as social network analysis and bioinformatics. Traditional methods typically focus on the topological structure of networks at a specific level, but they may overlook important properties exhibited by many networks, such as scale-free properties and specific power-law structures often found in social networks. Consequently, these methods fail to effectively capture and utilize such information, leading to misalignment. In this article, we propose a network alignment framework that incorporates both topological and attribute information from multiple levels in the network, including homogeneity, power-law, and higher order structures. We introduce a Euclidean hyperbolic interactive graph learning method specifically designed for modeling power-law structures in networks, aiming to improve the accuracy of network alignment. To evaluate the effectiveness of our proposed method, we conduct experiments on several real-world datasets. The results demonstrate that our approach achieves higher accuracy compared to other advanced baselines.

Network alignment involves identifying corresponding nodes across multiple networks. The majority of existing methods adhere to the assumption of consistency. However, due to distinct graph generation mechanisms, anchor nodes in real-world datasets often exhibit more intricate structural patterns, such as having multiple different neighbors and higher-order associations. Relying solely on consistency while disregarding the intricate patterns of anchor links may potentially inflict substantial detriment upon both the accuracy of network alignment and the generality of the model. In this paper, we introduce the disparity and diversity based on distinct structural patterns of ubiquitous anchor links. We propose a comprehensive framework that employs first-order proximity, lower-order discriminability, and higher-order correlation to model consistency, disparity, and diversity. We also incorporate a post-fusion mechanism for effectively integrating alignment matrices. Furthermore, we innovatively introduce hyperbolic space as an embedding space to further minimize embedding distortion. Extensive experiments have shown that our approach achieves state-of-the-art alignment results and yields notable improvements in the overall versatility of the model.