  We present a simple proof for the universality of invariant and equivariant
tensorized graph neural networks. Our approach considers a restricted
intermediate hypothetical model named Graph Homomorphism Model to reach the
universality conclusions including an open case for higher-order output. We
find that our proposed technique not only leads to simple proofs of the
universality properties but also gives a natural explanation for the
tensorization of the previously studied models. Finally, we give some remarks
on the connection between our model and the continuous representation of
graphs.
