  Graph embedding is gaining its popularity for link prediction in complex
networks and achieving excellent performance. However, limited work has been
done in sparse networks that represent most of real networks. In this paper, we
propose a model, Sparse Structural Network Embedding (SSNE), to obtain node
representation for link predication in sparse networks. The SSNE first
transforms the adjacency matrix into the Sum of Normalized $H$-order Adjacency
Matrix (SNHAM), and then maps the SNHAM matrix into a $d$-dimensional feature
matrix for node representation via a neural network model. The mapping
operation is proved to be an equivalent variation of singular value
decomposition. Finally, we calculate nodal similarities for link prediction
based on such feature matrix. By extensive testing experiments bases on
synthetic and real sparse network, we show that the proposed method presents
better link prediction performance in comparison of those of structural
similarity indexes, matrix optimization and other graph embedding models.
