Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization, node classification, and language modeling. In recent years, the field of graph embedding has witnessed a shift from linear algebraic approaches towards local, gradient-based optimization methods combined with random walks and deep neural networks to tackle the problem of embedding large graphs. However, despite this improvement in the optimization tools, graph embedding methods are still generically designed in a way that is oblivious to the particularities of real-life networks. Indeed, there has been significant progress in understanding and modeling complex real-life networks in recent years. However, the obtained results have had a minor influence on the development of graph embedding algorithms. This paper aims to remedy this by designing a graph embedding method that takes advantage of recent valuable insights from the field of network science. More precisely, we present a novel graph embedding approach based on the popularity-similarity and local attraction paradigms. We evaluate the performance of the proposed approach on the link prediction task on a large number of real-life networks. We show, using extensive experimental analysis, that the proposed method outperforms state-of-the-art graph embedding algorithms. We also demonstrate its robustness to data scarcity and the choice of embedding dimensionality.