# K dimensional WL test in K-WL GCN

I am reading a paper on the K-WL GCN. I did not complete the paper yet but I just skimmed over it. There I am trying to understand the K-WL test (page 3 Weisfeiler-Leman Algorithm). I think my understanding is quite ambiguous, so I looking for an example problem that is solved using K-WL test. But I can't find any of them on the web.

Does anyone have any solved example problem on K-WL or can anyone explain to me how the K-WL test works?

Note: If anyone also explains how K-WL GCN uses the K-WL test, I will be thankful.

• Thanks for the answer. I have few questions regarding the answer:1)Is the neighborhood of a $K$-triplet must belong to the set $V^K$. 2) Does the ordering of the triplet (for example (a,b,c) or (b,c,a)) matter? 2)In K-WL GCN, How we define input features for $K$-triplet since we have only input features for each node? – Swakshar Deb Mar 25 at 17:01