  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.
