  Graph embeddings have become a key and widely used technique within the field
of graph mining, proving to be successful across a broad range of domains
including social, citation, transportation and biological. Graph embedding
techniques aim to automatically create a low-dimensional representation of a
given graph, which captures key structural elements in the resulting embedding
space. However, to date, there has been little work exploring exactly which
topological structures are being learned in the embeddings process. In this
paper, we investigate if graph embeddings are approximating something analogous
with traditional vertex level graph features. If such a relationship can be
found, it could be used to provide a theoretical insight into how graph
embedding approaches function. We perform this investigation by predicting
known topological features, using supervised and unsupervised methods, directly
from the embedding space. If a mapping between the embeddings and topological
features can be found, then we argue that the structural information
encapsulated by the features is represented in the embedding space. To explore
this, we present extensive experimental evaluation from five state-of-the-art
unsupervised graph embedding techniques, across a range of empirical graph
datasets, measuring a selection of topological features. We demonstrate that
several topological features are indeed being approximated by the embedding
space, allowing key insight into how graph embeddings create good
representations.
