A general deep-learning approach to node importance identification

Identifying key nodes is an important task of complex network. While many previous algorithms evaluate node importance from the perspective of the network topological properties such as degree or betweenness, they have not considered the low-dimensional feature of nodes. In this paper, we propose a general improved approach based on deep learning, in which the node feature is learned via a variational graph auto-encoder(VGAE). Due to the unsupervised learning way, the VGAE does not rely on any external label information, but is determined by the network structure. The extracted node feature provides an essential complement to the topological properties of nodes, and can be generalized to improve different algorithms. We employ the VGAE to improve ten distinct algorithms, which are evaluated by two accuracy indicators using the susceptible–infected–recovered (SIR) model around the epidemic threshold as the benchmark, and an indicator of the significance discrimination ability on the nodes with similar importance. Testing the algorithms on an ER random network and eight real networks, we demonstrate better performance of the ten improved algorithms than their original ones in most cases. Our work sheds a new light on node importance identification from the latent feature point of view.