Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence.

翻译：图神经网络（GNN）是一类用于图处理的关系模型。近期关于GNN表达能力的理论研究成果聚焦于两个方向：一方面，已证明GNN在区分图的能力上与Weisfeiler-Lehman测试（1-WL）具有同等效力，且1-WL等价性与展开等价性具有一致性；另一方面，GNN在1-WL/展开等价性约束下可成为图上的通用逼近器。然而，上述结论仅适用于含节点属性的静态无向同质图（SAUHG）。实际应用场景往往涉及更丰富的图类型。本文针对两类具有重要实践价值的图域开展GNN表达能力理论分析：动态图与含边属性的SAUHG。动态图在现代应用中广泛存在，研究该域中GNN的表达能力不仅具有实践意义，更因其与静态GNN架构差异而需采用新型分析方法。同时，SAUHG的研究具有特殊重要性——它作为所有图类型的标准化形式，已被证明各类图均可在无信息损失条件下转化为具有节点与边双重属性的SAUHG。本文为上述图域构建通用GNN模型及相应1-WL测试，并将已知GNN表达能力结论拓展至新域：证明GNN与1-WL测试具有同等效力，1-WL等价性等同于展开等价性，且GNN在1-WL/展开等价性约束下可作为通用逼近器。