Hyperbolic Geometry of Complex Networks

@article{Krioukov2010HyperbolicGO,
  title={Hyperbolic Geometry of Complex Networks},
  author={Dmitri V. Krioukov and Fragkiskos Papadopoulos and Maksim Kitsak and Amin Vahdat and Mari{\'a}n Bogu{\~n}{\'a}},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2010},
  volume={82 3 Pt 2},
  pages={
          036106
        }
}
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is… 
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