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Graph embedding is a technique which consists in finding a new representation for a graph usually by representing the nodes as vectors in a low-dimensional real space. In this paper, we compare some of the best known algorithms proposed over the last few years, according to four structural properties of graphs: first-order and second-order proximities, isomorphic equivalence and community membership. To study the embedding algorithms, we introduced several measures. We show that most of the algorithms are able to recover at most one of the properties and that some algorithms are more sensitive to the embedding space dimension than some others.

Comparing the Preservation of Network Properties by Graph Embeddings