Expectation Complete Graph Representations using Graph Homomorphisms

Maximilian Thiessen, Pascal Welke, Thomas Gärtner

Keywords: graph embeddings, expressiveness, graph homomorphisms

TL;DR: We propose and study a practical graph embedding that in expectation is able to distinguish all non-isomorphic graphs and can be computed in polynomial time.

Abstract: We propose and study a practical graph embedding that *in expectation* is able to distinguish all non-isomorphic graphs and can be computed in polynomial time. The embedding is based on Lovász' characterization of graph isomorphism through an infinite dimensional vector of homomorphism counts. Recent work has studied the expressiveness of graph embeddings by comparing their ability to distinguish graphs to that of the Weisfeiler-Leman hierarchy. While previous methods have either limited expressiveness or are computationally impractical, we devise efficient sampling-based alternatives that are maximally expressive in expectation. We empirically evaluate our proposed embeddings and show competitive results on several benchmark graph learning tasks.

Community Implementations: [ 4 code implementations](https://www.catalyzex.com/paper/expectation-complete-graph-representations/code)