  In this paper we further develop the ideas from Geometric Function Theory
initially introduced in [arXiv:2206.13206], to derive capacity estimate in
metastability for arbitrary configurations. The novelty of this paper is
twofold. First, the graph theoretical connection enables us to exactly compute
the pre-factor in the capacity. Second, we complete the method from
[arXiv:2206.13206] by providing an upper bound using Geometric Function Theory
together with Thompson's principle, avoiding explicit constructions of test
functions.
