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We consider the problem of embedding an undirected graph into hyperbolic space with minimum distortion. A fundamental problem in its own right, it has also drawn a great deal of interest from applied communities interested in empirical analysis of large-scale graphs. In this paper, we establish a connection between distortion and quasi-cyclicity of graphs, and use it to derive lower and upper bounds on metric distortion. Two particularly simple and natural graphs with large quasi-cyclicity are n-node cycles and n × n square lattices, and our lower bound shows that any hyperbolic-space embedding of these graphs incurs a multiplicative distortion of at least Ω(n/log n). This is in sharp contrast to Euclidean space, where both of these graphs can be embedded with only constant multiplicative distortion. We also establish a relation between quasi-cyclicity and δ-hyperbolicity of a graph as a way to prove upper bounds …