We introduce a method for embedding graphs as vectors in a structure-preserving manner, showcasing its rich representational capacity and giving some theoretical properties. Our procedure falls under the bind-and-sum approach, and we show that our binding operation - the tensor product - is the most general binding operation that respects the principle of superposition. 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. Then, we perform experiments showcasing our method's accuracy in various graph operations even when the number of edges is quite large. Finally, we establish a link to adjacency matrices, showing that our method is, in some sense, a generalization of adjacency matrices with applications towards large sparse graphs.

翻译：我们提出了一种以保持结构的方式将图嵌入为向量的方法，展示了其丰富的表示能力并给出了若干理论性质。该流程属于“绑定与求和”框架，并证明我们的绑定运算——张量积——是尊重叠加原理的最通用绑定运算。我们还建立了刻画该方法行为的精确结果，并展示了球面码的使用达到了堆积上界。随后，通过实验展示了该方法在图运算中的准确性，即使边数非常大时仍表现良好。最后，我们建立了与邻接矩阵的联系，表明该方法在某种意义上是对邻接矩阵的推广，可用于大规模稀疏图。