  We demonstrate that the self-similarity of some scale-free networks with
respect to a simple degree-thresholding renormalization scheme finds a natural
interpretation in the assumption that network nodes exist in hidden metric
spaces. Clustering, i.e., cycles of length three, plays a crucial role in this
framework as a topological reflection of the triangle inequality in the hidden
geometry. We prove that a class of hidden variable models with underlying
metric spaces are able to accurately reproduce the self-similarity properties
that we measured in the real networks. Our findings indicate that hidden
geometries underlying these real networks are a plausible explanation for their
observed topologies and, in particular, for their self-similarity with respect
to the degree-based renormalization.
