Evaluating the quality of graph embeddings via topological feature reconstruction

In this paper we study three state-of-the-art, but competing, approaches for generating graph embeddings using unsupervised neural networks. Graph embeddings aim to discover the 'best' representation for a graph automatically and have been applied to graphs from numerous domains, including social networks. We evaluate their effectiveness at capturing a good representation of a graph's topological structure by using the embeddings to predict a series of topological features at the vertex level. We hypothesise that an 'ideal' high quality graph embedding should be able to capture key parts of the graph's topology, thus we should be able to use it to predict common measures of the topology, for example vertex centrality. This could also be used to better understand which topological structures are truly being captured by the embeddings. We first review these three graph embedding techniques and then evaluate how close they are to being 'ideal'. We provide a framework, with extensive experimental evaluation on empirical and synthetic datasets, to assess the effectiveness of several approaches at creating graph embeddings which capture detailed topological structure.