| Summary: | Graph embedding is gaining popularity for link prediction in complex networks. However, few works focus on the effectiveness of graph embedding models on link prediction in sparse networks. This paper proposes a novel graph embedding model, <bold>S</bold>parse <bold>S</bold>tructural <bold>N</bold>etwork <bold>E</bold>mbedding (SSNE), to obtain node representation for link predication in sparse networks. The SSNE first transforms the adjacency matrix into the <bold>S</bold> <inline-formula> <tex-math notation="LaTeX">$\mu {\mathrm{ m}}$ </tex-math></inline-formula> of <bold>N</bold>ormalized <bold>H</bold>-order <bold>A</bold>djacency <bold>M</bold>atrix (SNHAM) and then maps the SNHAM matrix into a <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-dimensional feature matrix for node representation via a neural network model. The mapping operation is proved to be an equivalent variety of singular value decomposition. Finally, we calculate nodal similarities for link prediction based on the <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-dimensional feature matrix. The extensive testing experiments based on artificial and real sparse networks suggest that the SSNE shows the effective node representation for link prediction in sparse networks, supported by the better link prediction performance compared to those of structural similarity indexes, matrix optimization, and other graph embedding models.
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