  In this work we produce a framework for constructing universal function
approximators on graph isomorphism classes. We prove how this framework comes
with a collection of theoretically desirable properties and enables novel
analysis. We show how this allows us to achieve state-of-the-art performance on
four different well-known datasets in graph classification and separate classes
of graphs that other graph-learning methods cannot. Our approach is inspired by
persistent homology, dependency parsing for NLP, and multivalued functions. The
complexity of the underlying algorithm is O(#edges x #nodes) and code is
publicly available
(https://github.com/bruel-gabrielsson/universal-function-approximation-on-graphs).
