Network embedding with centrality information

Information networks such as social networks, publication networks, and the World Wide Web are ubiquitous in the real world. Traditionally, adjacency matrices are used to represent the networks. However, adjacency matrices are too sparse and too high dimensional when the scale of the networks is large. Network embedding, which aims to learn low-dimensional continuous representations for nodes, has attracted increasing attention recent years. Many network embedding methods such as DeepWalk, LINE, and node2vec have been proposed recently. Many traditional tasks such as node classification and link prediction have been proven to be benefited from the learned representations. Most of these existing network embedding methods focus on preserving the structure of the networks but totally ignore the centrality information. Centrality information which measures the importance of each individual node has been proven to be helpful in many applications. Various centrality measures such as degree centrality, closeness centrality, betweenness centrality, eigenvector centrality and Page-rank, have been proposed. Different centrality measures should be chosen according to different applications. In this paper, we aim to learn continuous nodes representations which can preserve not only the network structure but also the centrality information. We propose a general model to incorporate the centrality information in the sense of ranking. Different centrality measures can be used in the model.