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Carmesin, Federici, and Georgakopoulos [arXiv:1603.06712] constructed atransient hyperbolic graph that has no transient subtrees and that has theLiouville property for harmonic functions. We modify their construction to geta unimodular random graph with the same properties.

A unimodular Liouville hyperbolic souvlaki --- an appendix to [arXiv:1603.06712]