title: Curvature and temperature of complex networks.
abstract: 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.
authors.affiliation: Cooperative Association for Internet Data Analysis, University of California-San Diego, La Jolla, California 92093, USA.
authors.forename: Dmitri
authors.initials: D
authors.lastname: Krioukov
authors.forename: Fragkiskos
authors.initials: F
authors.lastname: Papadopoulos
authors.forename: Amin
authors.initials: A
authors.lastname: Vahdat
authors.forename: Marián
authors.initials: M
authors.lastname: Boguñá
mesh_terms: D003198:Computer Simulation; D008954:Models, Biological; D009415:Nerve Net / Q000502:physiology*; D015398:Signal Transduction / Q000502:physiology*; D013696:Temperature