  A novel class of graphs, here named quasiperiodic, are constructed via
application of the Horizontal Visibility algorithm to the time series generated
along the quasiperiodic route to chaos. We show how the hierarchy of
mode-locked regions represented by the Farey tree is inherited by their
associated graphs. We are able to establish, via Renormalization Group (RG)
theory, the architecture of the quasiperiodic graphs produced by irrational
winding numbers with pure periodic continued fraction. And finally, we
demonstrate that the RG fixed-point degree distributions are recovered via
optimization of a suitably defined graph entropy.
