This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we consider the case when these embeddings are real-valued. By viewing these embeddings as scalar functions on a domain of interest, we can utilize the tools available in persistent homology to study the topological information encoded in these representations. Our construction effectively defines a unique persistence-based graph descriptor, on both the graph and node levels, for every node representation algorithm. To demonstrate the effectiveness of the proposed method, we study the topological descriptors induced by DeepWalk, Node2Vec and Diff2Vec.

翻译：文章的目的是通过使用持续同系物中的现有工具来研究编译成节点图形表示式嵌入的表层属性。 具体地说, 根据一个节点嵌入代表算法, 当这些嵌入过程被真正估值时, 我们考虑这些案例。 通过将这些嵌入作为有兴趣领域的标值函数来看待, 我们可以使用在持续同系物中可用的工具来研究这些示意中编码的表层信息。 我们的构造有效地定义了每个节点代表算法在图表和节点级别上独特的基于持久性的图表描述符。 为了证明拟议方法的有效性, 我们研究了DeepWalk、Node2Vec 和 Diff2Vec 所引的表层描述符。