Network embedding is capable of providing low-dimensional feature representations for various machine learning applications. Current work focuses on: 1) designing the embedding as an unsupervised learning task to explicitly preserve the structural connectivity in the network or 2) generating the embedding as a by-product during the supervised learning of a specific discriminative task in a deep neural network. In this paper, we aim to take advantage of these two lines of research in the view of multi-output learning. That is, we propose a generative adversarial network embedding (GANE) model to adapt the generative adversarial framework to achieve the network embedding learning during the specific machine learning tasks. GANE has a generator to generate link edges, and a discriminator to distinguish the generated link edges from real connections (edges) in the network. Wasserstein-1 distance is adopted to train the generator to gain better stability. GANE is further extended by utilizing the pairwise connectivity of vertices to preserve the structural information in the original network. Experiments with real-world network data sets demonstrate that our models constantly outperform state-of-the-art solutions with significant improvements for the tasks of link prediction, clustering, and network alignment.