Random geometric graphs have been well studied over the last 50 years or so. These are graphs that
are formed between points randomly allocated on a Euclidean space and any two of them are joined if
they are close enough. However, all this theory has been developed when the underlying space is
equipped with the Euclidean metric. But, what if the underlying space is curved?
The aim of this talk is to initiate the study of such random graphs and lead to the development of
their theory. Our focus will be on the case where the underlying space is a hyperbolic space. We
will discuss some typical structural features of these random graphs as well as some applications,
related to their potential as a model for networks that emerge in social life or in biological
sciences.