Graph matching problem aims to identify node correspondence between two or more correlated graphs. Previous studies have primarily focused on models where only edge information is provided. However, in many social networks, not only the relationships between users, represented by edges, but also their personal information, represented by features, are present. In this paper, we address the challenge of identifying node correspondence in correlated graphs, where additional node features exist, as in many real-world settings. We propose a two-step procedure, where we initially match a subset of nodes only using edge information, and then match the remaining nodes using node features. We derive information-theoretic limits for exact graph matching on this model. Our approach provides a comprehensive solution to the real-world graph matching problem by providing systematic ways to utilize both edge and node information for exact matching of the graphs.

翻译：图匹配问题旨在识别两个或多个相关图之间的节点对应关系。先前的研究主要集中于仅提供边信息的模型。然而，在许多社交网络中，不仅存在由边表示的用户关系，还存在由特征表示的用户个人信息。本文针对相关图中存在额外节点特征（如许多实际场景中的情况）时识别节点对应关系的挑战展开研究。我们提出一种两步流程：首先仅利用边信息匹配部分节点，随后利用节点特征匹配剩余节点。我们推导了该模型上精确图匹配的信息论极限。通过提供系统化利用边与节点信息实现图精确匹配的方法，我们的研究为现实世界图匹配问题提供了全面解决方案。