  We consider two non-degenerate potentials for the quiver arising from the
once-punctured torus, which are a natural choice to study and compare: the
first is the Labardini-potential, yielding a finite-dimensional Jacobian
algebra, whereas the second potential gives rise to an infinite dimensional
Jacobian algebra. In this paper we determine the graph of strongly reduced
components for both Jacobian algebras. Our main result is that the graph is
connected in both cases. Plamondon parametrized the strongly reduced components
for finite-dimensional algebras using generic g-vectors. We prove that the
generic g-vectors of indecomposable strongly reduced components of the
finite-dimensional Jacobian algebra are precisely the universal geometric
coefficients for the once-punctured torus, which were determined by Reading.
