  We present applications of the renormalization algorithm with graph
enhancement (RAGE). This analysis extends the algorithms and applications given
for approaches based on matrix product states introduced in [Phys. Rev. A 79,
022317 (2009)] to other tensor-network states such as the tensor tree states
(TTS) and projected entangled pair states (PEPS). We investigate the
suitability of the bare TTS to describe ground states, showing that the
description of certain graph states and condensed matter models improves. We
investigate graph-enhanced tensor-network states, demonstrating that in some
cases (disturbed graph states and for certain quantum circuits) the combination
of weighted graph states with tensor tree states can greatly improve the
accuracy of the description of ground states and time evolved states. We
comment on delineating the boundary of the classically efficiently simulatable
states of quantum many-body systems.
