Embedding social network data into a low-dimensional vector space has shown promising performance for many real-world applications, such as node classification, node clustering, link prediction and network visualization. However, the information contained in these vector embeddings remains abstract and hard to interpret. Methods for inspecting embeddings usually rely on visualization methods, which do not work on a larger scale and do not give concrete interpretations of vector embeddings in terms of preserved network properties (e.g., centrality or betweenness measures). In this paper, we study and investigate network properties preserved by recent random walk-based embedding procedures like node2vec, DeepWalk or LINE. We propose a method that applies learning to rank in order to relate embeddings to network centralities. We evaluate our approach with extensive experiments on real-world and artificial social networks. Experiments show that each embedding method learns different network properties. In addition, we show that our graph embeddings in combination with neural networks provide a computationally efficient way to approximate the Closeness Centrality measure in social networks.
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