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Extracting information from real-world large networks is a key challenge nowadays. For instance, computing a node centrality may become unfeasible depending on the intended centrality due to its computational cost. One solution is to develop fast methods capable of approximating network centralities. Here, we propose an approach for efficiently approximating node centralities for large networks using Neural Networks and Graph Embedding techniques. Our proposed model, entitled Network Centrality Approximation using Graph Embedding (NCA-GE), uses the adjacency matrix of a graph and a set of features for each node (here, we use only the degree) as input and computes the approximate desired centrality rank for every node. NCA-GE has a time complexity of $O(|E|)$, $E$ being the set of edges of a graph, making it suitable for large networks. NCA-GE also trains pretty fast, requiring only a set of a thousand small synthetic scale-free graphs (ranging from 100 to 1000 nodes each), and it works well for different node centralities, network sizes, and topologies. Finally, we compare our approach to the state-of-the-art method that approximates centrality ranks using the degree and eigenvector centralities as input, where we show that the NCA-GE outperforms the former in a variety of scenarios.