There are pairs of non-isomorphic graphs that are indistinguishable by the k-WL (but distinguishable by (k+1)-WL) . For example 4x4 rook’s graph and the Shrikhande graph are non-isomorphic but the 3-WL test cannot distinguish them .
I'm specifically looking for two non-isomorphic graphs that are indistinguishable by the 4-WL test. Are there two graphs with adjacency matrices in the literature, or existing implementations of  to generate such graphs?
 Cai, J. Y., Fürer, M., & Immerman, N. (1992). An optimal lower bound on the number of variables for graph identification. Combinatorica, 12(4), 389-410.
 Arvind, V., Fuhlbrück, F., Köbler, J., & Verbitsky, O. (2020). On Weisfeiler-Leman invariance: Subgraph counts and related graph properties. Journal of Computer and System Sciences, 113, 42-59.