  This paper focuses on studying the configuration spaces of graphs realised in
$\mathbb C^2$, such that the configuration space is, after normalisation, one
dimensional. If this is the case, then the configuration space is, generically,
a smooth complex curve, and can be seen as a Riemann surface. The property of
interest in this paper is the genus of this curve. Using tropical geometry, we
give an algorithm to compute this genus. We provide an implementation in Python
and give various examples.
