Network alignment, the problem of identifying similar nodes across networks, is an emerging research topic due to its ubiquitous applications in many data domains such as social-network reconciliation and protein-network analysis. While traditional alignment methods struggle to scale to large graphs, the state-of-the-art representation-based methods often rely on pre-defined anchor links, which are unavailable or expensive to compute in many applications. In this paper, we propose NAWAL, a novel, end-to-end unsupervised embedding-based network alignment framework emphasizing on structural information. The model first embeds network nodes into a low-dimension space where the structural neighborhoodship on original network is captured by the distance on the space. As the space for the input networks are learnt independently, we further leverage a generative adversarial deep neural network to reconcile the spaces without relying on hand-crafted features or domain-specific supervision. The empirical results on three real-world datasets show that NAWAL significantly outperforms state-of-the-art baselines, by over 13% of accuracy against unsupervised methods and on par or better than supervised methods. Our technique also demonstrate the robustness against adversarial conditions, such as structural noises and graph size imbalance.