α_i-metric graphs are f(i)-hyperbolic for linear f; α_1-metric graphs are exactly 1-hyperbolic while 1-hyperbolic graphs need not be α_i-metric for any fixed i.
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$\alpha_i$-Metric Graphs: Hyperbolicity
α_i-metric graphs are f(i)-hyperbolic for linear f; α_1-metric graphs are exactly 1-hyperbolic while 1-hyperbolic graphs need not be α_i-metric for any fixed i.