We introduce a method for embedding graphs as vectors in a structure-preserving manner. In this paper, we showcase its rich representational capacity and give some theoretical properties of our method. In particular, 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. Similarly, we show that the spherical code achieves optimal compression. We then establish some precise results characterizing the performance our method as well as some experimental results showcasing how it can accurately perform various graph operations even when the number of edges is quite large. Finally, we conclude with establishing 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：我们引入了一种将图形嵌入为矢量的方法。 在本文中, 我们展示了它丰富的代表能力, 并给出了我们方法的一些理论属性。 特别是, 我们的程序属于约束和总和方法, 我们展示了我们的约束操作 — — 高压产品 — — 是尊重叠加原则的最普遍的约束操作。 同样, 我们展示了球形代码实现了最佳压缩。 然后, 我们确定了一些精确的结果来描述我们方法的性能特征, 以及一些实验结果, 展示了即使边缘数量相当大, 我们如何精确地执行各种图形操作。 最后, 我们以建立与相邻矩阵的链接结束, 表明我们的方法在某种意义上是将相邻矩阵与大稀薄图的应用相近。