  We show that heterogeneous degree distributions in observed scale-free
topologies of complex networks can emerge as a consequence of the exponential
expansion of hidden hyperbolic space. Fermi-Dirac statistics provides a
physical interpretation of hyperbolic distances as energies of links. The
hidden space curvature affects the heterogeneity of the degree distribution,
while clustering is a function of temperature. We embed the Internet into the
hyperbolic plane, and find a remarkable congruency between the embedding and
our hyperbolic model. Besides proving our model realistic, this embedding may
be used for routing with only local information, which holds significant
promise for improving the performance of Internet routing.
