  In the past decade, geometric network models have received vast attention in
the literature. These models formalize the natural idea that similar vertices
are likely to connect. Because of that, these models are able to adequately
capture many common structural properties of real-world networks, such as
self-invariance and high clustering. Indeed, many real-world networks can be
accurately modeled by positioning vertices of a network graph in hyperbolic
spaces. Nevertheless, if one observes only the network connections, the
presence of geometry is not always evident. Currently, triangle counts and
clustering coefficients are the standard statistics to signal the presence of
geometry. In this paper we show that triangle counts or clustering coefficients
are insufficient because they fail to detect geometry induced by hyperbolic
spaces. We therefore introduce a novel triangle-based statistic, which weighs
triangles based on their strength of evidence for geometry. We show
analytically, as well as on synthetic and real-world data, that this is a
powerful statistic to detect hyperbolic geometry in networks.
