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Word and graph embeddings are widely used in deep learning applications. Wepresent a data structure that captures inherent hierarchical properties from anunordered flat embedding space, particularly a sense of direction between pairsof entities. Inspired by the notion of \textit{distributional generality}, ouralgorithm constructs an arborescence (a directed rooted tree) by insertingnodes in descending order of entity power (e.g., word frequency), pointing eachentity to the closest more powerful node as its parent.  We evaluate the performance of the resulting tree structures on three tasks:hypernym relation discovery, least-common-ancestor (LCA) discovery among words,and Wikipedia page link recovery. We achieve average 8.98\% and 2.70\% forhypernym and LCA discovery across five languages and 62.76\% accuracy ondirected Wiki-page link recovery, with both substantially above baselines.Finally, we investigate the effect of insertion order, the power/similaritytrade-off and various power sources to optimize parent selection.

Hierarchies over Vector Space: Orienting Word and Graph Embeddings