Volume 81, Number 3, February 2008
|Number of page(s)||5|
|Published online||31 December 2007|
Transition from small to large world in growing networks
Departamento de Física da Universidade de Aveiro - 3810-193 Aveiro, Portugal
2 A. F. Ioffe Physico-Technical Institute - 194021 St. Petersburg, Russia
3 Department of Physics and Center for Molecular Cybernetics, Boston University - Boston, MA 02215, USA
Accepted: 26 November 2007
We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite or finite dimensional depending on whether the attachment probability decays slower or faster than (age)-1. The network becomes one dimensional when the attachment probability decays faster than (age)-2. We describe structural characteristics of these phases and transitions between them.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.75.Fb – Structures and organization in complex systems / 89.75.Hc – Networks and genealogical trees
© EPLA, 2008
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