Issue
EPL
Volume 81, Number 3, February 2008
Article Number 30004
Number of page(s) 5
Section General
DOI http://dx.doi.org/10.1209/0295-5075/81/30004
Published online 31 December 2007
EPL, 81 (2008) 30004
DOI: 10.1209/0295-5075/81/30004

Transition from small to large world in growing networks

S. N. Dorogovtsev1, 2, P. L. Krapivsky3 and J. F. F. Mendes1

1  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


received 19 September 2007; accepted in final form 26 November 2007; published February 2008
published online 31 December 2007

Abstract
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