Motivated by various data science applications including de-anonymizing user identities in social networks, we consider the graph alignment problem, where the goal is to identify the vertex/user correspondence between two correlated graphs. Existing work mostly recovers the correspondence by exploiting the user-user connections. However, in many real-world applications, additional information about the users, such as user profiles, might be publicly available. In this paper, we introduce the attributed graph alignment problem, where additional user information, referred to as attributes, is incorporated to assist graph alignment. We establish both the achievability and converse results on recovering vertex correspondence exactly, where the conditions match for a wide range of practical regimes. Our results span the full spectrum between models that only consider user-user connections and models where only attribute information is available.

翻译：受多种数据科学应用（包括社交网络中用户身份去匿名化）的推动，我们研究了图对齐问题，其目标是在两个相关图之间识别顶点/用户对应关系。现有工作大多通过利用用户-用户连接来恢复对应关系。然而，在许多实际应用中，关于用户的额外信息（如用户资料）可能是公开可获取的。本文引入了属性化图对齐问题，其中整合了称为属性的额外用户信息以辅助图对齐。我们建立了精确恢复顶点对应关系的可达性与逆结果，且该条件在广泛实际场景中达到匹配。我们的结果覆盖了仅考虑用户-用户连接的模型与仅利用属性信息的模型之间的完整谱系。