A random geometric graph $G_n$ is constructed by taking vertices $X_1,
..., X_n \in R^d$ at random (i.i.d.~according to some probability
distribution nu$$\) and including an edge between $X_i$ and $X-j$ if
$|X_i-X_j| < r$ where $r=r(n) > 0$.
We prove a conjecture of Penrose stating that when $n r^d = o(\ln n)$ then
the probability distribution of the clique number $\omega(G_n)$ becomes
concentrated on two consecutive integers in the sense that ${\mathbb
P}(\omega(G_n) ∈ \{k(n), k(n)+1\} )$ tends to 1 for some sequence
$k(n)$.
We also show that the same holds for a number of other graph parameters
including the chromatic number $\chi(G_n)$. A series of celebrated results
establish that a similar phenomenon occurs in the Erd\H{o}s-R\'enyi or
$G(n,p)$-model of random graphs.