Characterizing the Expressive Power of the Weisfeiler-Leman Test for Counting Graph Motifs

The Weisfeiler-Leman (WL) test is a powerful method for verifying graph isomorphism, and its connection to the expressive capabilities of graph neural networks has sparked significant interest in understanding the specific graph properties that the WL test can effectively distinguish. This paper provides a precise characterization of the WL-dimension of labeled graph motif parameters, which unifies the study of subgraph counting and induced subgraph counting problems.