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.

翻译：我们分析了一种以保持结构的方式将图嵌入为向量的方法，展示了其丰富的表征能力，并确立了其部分理论性质。所提出的方法属于绑定-求和框架，我们证明张量积是满足叠加原理的最通用的绑定操作。我们还建立了若干精确结果来刻画该方法的行为，并表明采用球面编码可实现空间堆积上界。我们建立了该方法与邻接矩阵之间的联系，证明其在某种意义上是对邻接矩阵的一种压缩，可应用于稀疏图表示。