Graph autoencoder for directed weighted network

Network embedding technology transforms network structure into node vectors, which reduces the complexity of representation and can be effectively applied to tasks such as classification, network reconstruction and link prediction. The main concern of network embedding is to keep the local structural features while effectively capturing the global features of the network. The "shallow" network representation models cannot capture the deep nonlinear features of the network, and the generated network embedding is usually not the optimal solution. In this paper, a new graph autoencoder-based network representation model combines the first- and second-order proximity to evaluate the performance of network embedding. Aiming at the shortcomings of existing network representation methods in weighted and directed networks, on one hand, the concepts of receiving vector and sending vector are introduced with a simplification of decoding part of the neural network which reduces computation complexity; on the other hand, a measurement index based on node degree is proposed to better emphasize the weighted information in the application of network representation. Experiments including directed weighted networks and undirected unweighted networks show that the proposed method achieves better results than the baseline methods for network reconstruction and link prediction tasks and is of higher computation efficiency than previous graph autoencoder algorithms. Besides, the proposed weighted index is able to improve performances of all baseline methods as an external assistance.