  It has recently been shown that the TIP4P/Ice model of water can be studied
numerically in metastable equilibrium at and below its liquid-liquid critical
temperature. We report here simulations along a subcritical isotherm, for which
two liquid states with the same pressure and temperature, but different
density, can be equilibrated. This allows for a clear visualisation of the
structural changes taking place across the transition. We specifically focus on
how the topological properties of the H-bond network change across the
liquid-liquid transition. Our results demonstrate that the structure of the
high-density liquid, characterised by the existence of interstitial molecules
and commonly explained in terms of the collapse of the second neighbour shell,
actually originates from the folding back of long rings, bringing pairs of
molecules separated by several hydrogen-bonds close by in space.
