  In this contribution we study the onset of chaos via type-II intermittency
within the framework of Horizontal Visibility graph theory. We construct graphs
associated to time series generated by an iterated map close to a
Neimark-Sacker bifurcation and study, both numerically and analytically, their
main topological properties. We find well defined equivalences between the main
statistical properties of intermittent series (scaling of laminar trends and
Lyapunov exponent) and those of the resulting graphs, and accordingly construct
a graph theoretical description of type-II intermittency. We finally recast
this theory into a graph-theoretical renormalization group framework, and show
that the fixed point structure of RG flow diagram separates regular, critical
and chaotic dynamics.
