  Answering a question of Wright, we show that spheres of any radius are always
connected in the curve graph of surfaces $\Sigma_{2,0}, \Sigma_{1,3},$ and
$\Sigma_{0,6}$, and the union of two consecutive spheres is always connected
for $\Sigma_{0, 5}$ and $\Sigma_{1,2}$. We also classify the connected
components of spheres of radius 2 in the curve graph of $\Sigma_{0, 5}$ and
$\Sigma_{1,2}$.
