  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.
