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
c
and radius
r
r
, we define the sphere of radius
r
r
to be the induced subgraph on the set of vertices of distance
r
r
from
c
c
. We show that these spheres are always connected in high enough complexity, and prove a slightly weaker result for low complexity surfaces.