  This work addresses a modification of the random geometric graph (RGG) model
by considering a set of points uniformly and independently distributed on the
surface of a $(d-1)$-sphere with radius $r$ in a $d-$dimensional Euclidean
space, instead of on an unit hypercube $[0,1]^d$ . Then, two vertices are
connected by a link if their great circle distance is at most $s$. In the case
of $d=3$, the topological properties of the random spherical graphs (RSGs)
generated by this model are studied as a function of $s$. We obtain analytical
expressions for the average degree, degree distribution, connectivity, average
path length, diameter and clustering coefficient for RSGs. By setting
$r=\sqrt{\pi}/(2\pi)$, we also show the differences between the topological
properties of RSGs and those of two-dimensional RGGs and random rectangular
graphs (RRGs). Surprisingly, in terms of the average clustering coefficient,
RSGs look more similar to the analytical estimation for RGGs than RGGs
themselves, when their boundary effects are considered. We support all our
findings by computer simulations that corroborate the accuracy of the
theoretical models proposed for RSGs.
