  We present an algorithm for computing the Berkovich skeleton of a
superelliptic curve $y^n=f(x)$ over a valued field. After defining
superelliptic weighted metric graphs, we show that each one is realizable by an
algebraic superelliptic curve when $n$ is prime. Lastly, we study the locus of
superelliptic weighted metric graphs inside the moduli space of tropical curves
of genus $g$.
