is concerned with either the behavior of a typical graph — the graph we are likely to see for a given $r$ as $n$ goes to infinity — or typical deviations from that behavior, i.e. central limit theorems. In this paper, we are concerned with the behavior of the model conditioned on a rare event. Specifically, we are concerned with the random geometric graph conditioned on having more edges than is expected (a formal description will follow). The large deviation regime of the upper tail of any subgraph count of the random geometric graph is not well studied, though some bounds are available: Janson [@Janson] has studied concentration inequalities for $U$-statistics, a general class of statistics which includes the subgraph counts we are interested in. These upper bounds work in very general settings, but are not tight, even up to constants in the exponent. Large deviation principles have been proven for functionals of random point processes in which the contribution of any particular vertex is uniformly bounded [@Schreiber], but no such bound is known for functionals with possibly large influence, such as the edge count of the graph.

As motivation for this detailed study, we consider the problem in a 