CINA: curvature-based integrated network alignment with hypergraph

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.