  Network models with latent geometry have been used successfully in many
applications in network science and other disciplines, yet it is usually
impossible to tell if a given real network is geometric, meaning if it is a
typical element in an ensemble of random geometric graphs. Here we identify
structural properties of networks that guarantee that random graphs having
these properties are geometric. Specifically we show that random graphs in
which expected degree and clustering of every node are fixed to some constants
are equivalent to random geometric graphs on the real line, if clustering is
sufficiently strong. Large numbers of triangles, homogeneously distributed
across all nodes as in real networks, are thus a consequence of network
geometricity. The methods we use to prove this are quite general and applicable
to other network ensembles, geometric or not, and to certain problems in
quantum gravity.
