  This study develops an algorithm to reproduce reaction route maps (RRMs) in
shape space from the outputs of potential search algorithms. To demonstrate
this, GRRM is utilized as a potential search algorithm but the proposed
algorithm should work with other potential search algorithms in principle. The
proposed algorithm does not require any encoding of the molecular
configurations and is thus applicable to complicated realistic molecules for
which efficient encoding is not readily available. We show subgraphs of a RRM
mapped to each other by the action of the symmetry group are isomorphic and
also provide an algorithm to compute the set of feasible transformations in the
sense of Longuet--Higgins. We demonstrate the proposed algorithm in toy models
and in more realistic molecules. Finally, we remark on absolute rate theory
from our perspective.
