  We consider the curve graph in the cases where it is not a Farey graph, and
show that its Gromov boundary is linearly connected. For a fixed center point c
and radius r, we define the sphere of radius r to be the induced subgraph on
the set of vertices of distance r from c. We show that these spheres are always
connected in high enough complexity, and prove a slightly weaker result for low
complexity surfaces.
