Graph Embeddings via Tensor Products and Approximately Orthonormal Codes

We analyze a method for embedding graphs as vectors in a structure-preserving manner, showcasing its rich representational capacity and establishing some of its theoretical properties. Our procedure falls under the bind-and-sum approach, and we show that the tensor product is the most general binding operation that respects the superposition principle. We also establish some precise results characterizing the behavior of our method, and we show that our use of spherical codes achieves a packing upper bound. We establish a link to adjacency matrices, showing that our method is, in some sense, a compression of adjacency matrices with applications towards sparse graph representations.