Volume 105, Number 3, February 2014
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||20 February 2014|
Duality between preferential attachment and static networks on hyperbolic spaces
1 Systématique, Adaptation et Evolution (UMR 7138), UPMC Univ Paris 06, CNRS, MNHN, IRD - Paris, France
2 CIRB, Collège de France - Paris, France
3 Dipartimento di Fisica, Università di Pisa - Pisa, Italy
4 Laboratoire d'Informatique de l'École Polytechnique (LIX) - Palaiseau, France
Received: 9 November 2013
Accepted: 23 January 2014
There is a complex relation between the mechanism of preferential attachment, scale-free degree distributions and hyperbolicity in complex networks. In fact, both preferential attachment and hidden hyperbolic spaces often generate scale-free networks. We show that there is actually a duality between a class of growing spatial networks based on preferential attachment on the sphere and a class of static random networks on the hyperbolic plane. Both classes of networks have the same scale-free degree distribution as the Barabasi-Albert model. As a limit of this correspondence, the Barabasi-Albert model is equivalent to a static random network on an hyperbolic space with infinite curvature.
PACS: 89.75.Hc – Networks and genealogical trees / 89.75.-k – Complex systems
© EPLA, 2014
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