Geodesic
How Much Topological Structure Is Preserved by Graph Embeddings?
Computer Science and Information Systems, Tome 16 (2019) no. 2.

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Graph embedding aims at learning representations of nodes in a low dimensional vector space. Good embeddings should preserve the graph topological structure. To study how much such structure can be preserved, we propose evaluation methods from four aspects: 1) How well the graph can be reconstructed based on the embeddings, 2) The divergence of the original link distribution and the embedding-derived distribution, 3) The consistency of communities discovered from the graph and embeddings, and 4) To what extent we can employ embeddings to facilitate link prediction. We find that it is insufficient to rely on the embeddings to reconstruct the original graph, to discover communities, and to predict links at a high precision. Thus, the embeddings by the state-of-the-art approaches can only preserve part of the topological structure.
Keywords: graph embedding, network representation learning, graph reconstruction, dimension reduction, graph mining 
@article{CSIS_2019_16_2_a12,
     author = {Xin Liu and Chenyi Zhuang and Tsuyoshi Murata and Kyoung-Sook Kim and Natthawut Kertkeidkachorn},
     title = {How {Much} {Topological} {Structure} {Is} {Preserved} by {Graph} {Embeddings?}},
     journal = {Computer Science and Information Systems},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2019},
     url = {http://geodesic.mathdoc.fr/item/CSIS_2019_16_2_a12/}
}
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Xin Liu; Chenyi Zhuang; Tsuyoshi Murata; Kyoung-Sook Kim; Natthawut Kertkeidkachorn. How Much Topological Structure Is Preserved by Graph Embeddings?. Computer Science and Information Systems, Tome 16 (2019) no. 2. http://geodesic.mathdoc.fr/item/CSIS_2019_16_2_a12/