Curvature and temperature of complex networks

Details Curvature and temperature of complex networks Curvature and temperature of complex networks

2009-03-14

arxiv.org/abs/0903.2584v2

Phys. Rev. E 80, 035101(R) (2009)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.80.035101

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.

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