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.

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• New Phenomena in Large-Scale Internet Traffic
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• Low-temperature behaviour of social and economic networks
• Features and heterogeneities in growing network models
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• Link persistence and conditional distances in multiplex networks
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• A Statistical Test of Walrasian Equilibrium by Means of Complex Networks Theory
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• Geometric evolution of complex networks
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