We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively avoiding troublesome embedding configurations (i.e. local minima) which can pose problems to non-convex optimization. HARP works by finding a smaller graph which approximates the global structure of its input. This simplified graph is used to learn a set of initial representations, which serve as good initializations for learning representations in the original, detailed graph. We inductively extend this idea, by decomposing a graph in a series of levels, and then embed the hierarchy of graphs from the coarsest one to the original graph. HARP is a general meta-strategy to improve all of the state-of-the-art neural algorithms for embedding graphs, including DeepWalk, LINE, and Node2vec. Indeed, we demonstrate that applying HARP's hierarchical paradigm yields improved implementations for all three of these methods, as evaluated on both classification tasks on real-world graphs such as DBLP, BlogCatalog, CiteSeer, and Arxiv, where we achieve a performance gain over the original implementations by up to 14%% Macro F1.