We investigate novel random graph embeddings that can be computed in expected polynomial time and are able to distinguish all non-isomorphic graphs *in expectation*. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrary expressive with increasing resources. Our approach is based on Lovász' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.