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Abstract: We show that heterogeneous degree distributions in observed scale-freetopologies of complex networks can emerge as a consequence of the exponentialexpansion of hidden hyperbolic space. Fermi-Dirac statistics provides aphysical interpretation of hyperbolic distances as energies of links. Thehidden space curvature affects the heterogeneity of the degree distribution,while clustering is a function of temperature. We embed the Internet into thehyperbolic plane, and find a remarkable congruency between the embedding andour hyperbolic model. Besides proving our model realistic, this embedding maybe used for routing with only local information, which holds significantpromise for improving the performance of Internet routing.



Author: Dmitri Krioukov, Fragkiskos Papadopoulos, Amin Vahdat, Marian Boguna

Source: https://arxiv.org/







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