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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper develops lower and upper bounds on the required rank of adjacency tensor factorizations to recover the adjacency tensor. This is, it investigates the problem of the minimal rank required to express the true underlying data via factorizations. These bounds are shown to of practical use by scaling RESCAL up. The paper is extremely well written and makes several interesting and important contributions.