  Suspensions of hard core spherical particles of diameter $D$ with inter-core
connectivity range $\delta$ can be described in terms of random geometric
graphs, where nodes represent the sphere centers and edges are assigned to any
two particles separated by a distance smaller than $\delta$. By exploiting the
property that closed loops of connected spheres becomes increasingly rare as
the connectivity range diminishes, we study continuum percolation of hard
spheres by treating the network of connected particles as having a treelike
structure for small $\delta/D$. We derive an analytic expression of the
percolation threshold which becomes increasingly accurate as $\delta/D$
diminishes, and whose validity can be extended to a broader range of
connectivity distances by a simple rescaling.
